Coordinate Geometry: 1 mark Questions (CBSE Class 10)

The distance between the points (– 4, 2) and (1, 0) is :

1. (A)$\sqrt{13}$ units
2. (B)3 units
3. (C)9 units
4. (D)$\sqrt{29}$ units

The distance between the points (– 5, 1) and (2, 2) is :

1. (A)$2\sqrt{5}$ units
2. (B)$\sqrt{10}$ units
3. (C)$5\sqrt{2}$ units
4. (D)$3\sqrt{2}$ units

The distance between the points (– 1, $2\sqrt{2}$) and (2, $\sqrt{2}$) is :

1. (A)$\sqrt{5}$ units
2. (B)$\sqrt{11}$ units
3. (C)$\sqrt{13}$ units
4. (D)$\sqrt{7}$ units

The distance between the points $(-2,5)$ and $(5,-2)$ is

1. (A)$7\sqrt{2}$
2. (B)14
3. (C)$2\sqrt{7}$
4. (D)7

The distance between the points $(-4,5)$ and $(-1,2)$ is

1. (A)5
2. (B)$3\sqrt{2}$
3. (C)6
4. (D)$2\sqrt{3}$

The mid-point of the line segment joining the points $(5,-4)$ and $(6,4)$ lies on :

1. (A)$x$-axis
2. (B)$y$-axis
3. (C)origin
4. (D)neither $x$-axis nor $y$-axis

The distance of the point A(4a, 3a) from x-axis is :

1. (A)3a
2. (B)$-3a$
3. (C)4a
4. (D)$-4a$

If the distance between the points (4, p) and (1, 0) is 5, then p is equal to :

1. (A)$\pm 4$
2. (B)4
3. (C)$-4$
4. (D)0

In the given figure, $\Delta$ ABC is an equilateral triangle. AD is a median of the triangle joining the points A$\left(0,\frac{5\sqrt{3}}{2}\right)$, D(0, 0). Points B and C are (in same order) :

1. (A)(– 5, 0), (5, 0)
2. (B)$\left(-\frac{5}{2},0\right),\left(\frac{5}{2},0\right)$
3. (C)(– 10, 0), (10, 0)
4. (D)$(-5\sqrt{3},0),(5\sqrt{3},0)$

In the given figure, a circle is centred at (1, 2). The diameter of the circle is

1. (A)4
2. (B)$2\sqrt{2}$
3. (C)$\sqrt{5}$
4. (D)$2\sqrt{5}$

The distance between the points $(a\cos \theta +b\sin \theta ,0)$ and $(0,a\sin \theta -b\cos \theta )$ is

1. (A)$\sqrt{a^2+b^2}$
2. (B)$a^2-b^2$
3. (C)$\sqrt{a^2-b^2}$
4. (D)$a^2+b^2$

A circle centred at $(-1,2)$ passes through the point (0, 3). Radius of the circle is

1. (A)$2\sqrt{2}$
2. (B)$\sqrt{2}$
3. (C)$\sqrt{26}$
4. (D)1

The line segment joining the points $P(-4,-2)$ and $Q(10,4)$ is divided by y-axis in the ratio

1. (A)2 : 5
2. (B)1 : 2
3. (C)2 : 1
4. (D)5 : 2

For a point $(3,-5)$, the value of (abscissa $-$ ordinate) is :

1. (A)$-8$
2. (B)$-2$
3. (C)2
4. (D)8

The mid-point of a line segment divides the line segment in the ratio :

1. (A)1 : 2
2. (B)2 : 1
3. (C)1 : 1
4. (D)$\frac{1}{2}$ : 2

The distance of a point $P(3,-7)$ from y-axis is :

1. (A)3
2. (B)7
3. (C)$-7$
4. (D)$\sqrt{58}$

For a point $X(a,b)$ where $(b>a>0)$, the value of its [distance from x-axis $-$ distance from y-axis] is :

1. (A)$a-b$
2. (B)$b-a$
3. (C)$a^2-b^2$
4. (D)$b^2-a^2$

The distance of the point (2, 3) from the origin is :

1. (A)$2$
2. (B)$3$
3. (C)$5$
4. (D)$\sqrt{13}$

The mid-point of the line segment joining points (1, 3) and (1, $-3$) lies :

1. (A)at the origin
2. (B)in the second quadrant
3. (C)on x-axis
4. (D)on y-axis

If point $(1,2)$ is the mid-point of the line segment joining the points $(3,5)$ and $(2a,b)$, then $(a,b)=$

1. (A)$(-1,-1)$
2. (B)$\left(-\frac{1}{2},-\frac{1}{2}\right)$
3. (C)$\left(-\frac{1}{2},-1\right)$
4. (D)$\left(-1,-\frac{1}{2}\right)$

The distance of point $(-3,4)$ from y-axis is :

1. (A)$-3$
2. (B)3
3. (C)4
4. (D)5

If point $(1,2)$ divides the line segment joining the points $(3,5)$ and $(2p,q)$ in the ratio $1:1$, then $(p,q)$ is equal to :

1. (A)$\left(-\frac{1}{2},-1\right)$
2. (B)$\left(-\frac{1}{2},-\frac{1}{2}\right)$
3. (C)$(-1,-1)$
4. (D)$\left(-1,-\frac{1}{2}\right)$

If point $(a,2b)$ is the mid-point of the line segment joining the points $(3,5)$ and $(-1,-1)$, then $(a,b)$ is equal to :

1. (A)$(1,2)$
2. (B)$(2,2)$
3. (C)$(2,1)$
4. (D)$(1,1)$

The distance between the points $(-6,9)$ and $(2,7)$ is :

1. (A)$2\sqrt{17}$
2. (B)$4\sqrt{17}$
3. (C)$2\sqrt{5}$
4. (D)$2\sqrt{15}$

The distance between the points $(2,-7)$ and $(-2,-1)$ is :

1. (A)10
2. (B)$2\sqrt{13}$
3. (C)8
4. (D)$4\sqrt{13}$

The distance between the points (2, 3) and (–2, –3) is

1. (A)$4\sqrt{13}$
2. (B)$\sqrt{40}$
3. (C)$2\sqrt{13}$
4. (D)5

The point ($x$, 0) divides the line segment joining the points (–4, 5) and (0, –10) in the ratio

1. (A)1 : 3
2. (B)2 : 1
3. (C)1 : 1
4. (D)1 : 2

If the distance between the points (3, 0) and (2, y) is $\sqrt{5}$, then the value(s) of y is :

1. (A)2, –2
2. (B)2, 0
3. (C)2, 1
4. (D)–2, 0

ABCD is a rectangle with its vertices at (2, $-2$), (8, 4), (4, 8) and ($-2$, 2) taken in order. Length of its diagonal is

1. (A)$4\sqrt{2}$
2. (B)$6\sqrt{2}$
3. (C)$4\sqrt{26}$
4. (D)$2\sqrt{26}$

The mid-point of the line segment joining the points $P(-4,5)$ and $Q(4,6)$ lies on :

1. (A)x-axis
2. (B)y-axis
3. (C)origin
4. (D)neither x-axis nor y-axis

The end points of a diameter of circle are $(2,4)$ and $(-3,-1)$. The length of its radius is :

1. (A)$\frac{5\sqrt{2}}{2}$ units
2. (B)$5\sqrt{2}$ units
3. (C)$3\sqrt{2}$ units
4. (D)$\pm \frac{5\sqrt{2}}{2}$ units

The coordinates of the end points of a diameter of a circle are $(5,-2)$ and $(5,2)$. The length of the radius of the circle is :

1. (A)$\pm 2$
2. (B)$\pm 4$
3. (C)4
4. (D)2

The points $(-5,0)$, $(5,0)$ and $(0,4)$ are the vertices of a triangle which is a/an :

1. (A)right-angled triangle
2. (B)isosceles triangle
3. (C)equilateral triangle
4. (D)scalene triangle

The perimeter of the triangle formed by the vertices $(0,0)$, $(2,0)$ and $(0,2)$ is :

1. (A)4 units
2. (B)6 units
3. (C)$6\sqrt{2}$ units
4. (D)$(4+2\sqrt{2})$ units

The line represented by $\frac{x}{4}+\frac{y}{6}=1$, intersects x-axis and y-axis respectively at P and Q. The coordinates of the mid-point of line segment PQ are :

1. (A)$(2,3)$
2. (B)$(3,2)$
3. (C)$(2,0)$
4. (D)$(0,3)$

Two of the vertices of $△PQR$ are $P(-1,5)$ and $Q(5,2)$. The coordinates of a point which divides PQ in the ratio $2:1$ are :

1. (A)$(3,-3)$
2. (B)$(5,5)$
3. (C)$(3,3)$
4. (D)$(5,1)$

AOBC is a rectangle whose three vertices are $A(0,2)$, $O(0,0)$ and $B(4,0)$. The square of the length of its diagonal is equal to :

1. (A)36
2. (B)20
3. (C)16
4. (D)4

If the mid-point of the line segment joining the points $(a,4)$ and $(2,2b)$ is $(2,6)$, then the value of $(a+b)$ is given by :

1. (A)6
2. (B)7
3. (C)8
4. (D)16

The distance of the point $(4,0)$ from x-axis is :

1. (A)4 units
2. (B)16 units
3. (C)0 units
4. (D)$4\sqrt{2}$ units

The distance of a point A from $x$-axis is 3 units. Which of the following cannot be coordinates of the point A ?

1. (A)$(1,3)$
2. (B)$(-3,-3)$
3. (C)$(-3,3)$
4. (D)$(3,1)$

The distance of which of the following points from origin is less than 5 units ?

1. (A)$(3,4)$
2. (B)$(2,6)$
3. (C)$(-3,-4)$
4. (D)$(1,4)$

The distance of point $P(1,-1)$ from $x$-axis is :

1. (A)1
2. (B)$-1$
3. (C)0
4. (D)$\sqrt{2}$

In the figure given below, points P, Q, R divides the line segment AB in four equal parts.
The point Q divides PB in the ratio

1. (A)1 : 3
2. (B)2 : 3
3. (C)1 : 2
4. (D)1 : 1

The point P divides the line segment AB in the ratio 3 : 1 as shown below :
The value of $\frac{AB}{PB}$ is

1. (A)3
2. (B)$\frac{1}{4}$
3. (C)4
4. (D)$\frac{1}{3}$

In the following figure, P and Q are points of trisection of line segment AB :
the value of $\frac{AB}{PB}=$

1. (A)1
2. (B)1.5
3. (C)$\frac{2}{3}$
4. (D)2

The distance of the point $A(-3,-4)$ from $x$-axis is

1. (A)3
2. (B)4
3. (C)5
4. (D)7

The distance of point $(a,-b)$ from $x$-axis is

1. (A)a
2. (B)$-a$
3. (C)b
4. (D)$-b$

The distance of point $P(3a,4a)$ from $y$-axis is

1. (A)3a
2. (B)$-3a$
3. (C)4a
4. (D)$-4a$

The distance between the points $(2,-3)$ and $(-2,3)$ is :

1. (A)$2\sqrt{13}$ units
2. (B)5 units
3. (C)$13\sqrt{2}$ units
4. (D)10 units

The diameter of a circle is of length 6 cm. If one end of the diameter is $(-4,0)$, the other end on x-axis is at :

1. (A)(0, 2)
2. (B)(6, 0)
3. (C)(2, 0)
4. (D)(4, 0)

The mid-point of the line segment joining the points $(-1,3)$ and $\left(8,\frac{3}{2}\right)$ is :

1. (A)$\left(\frac{7}{2},-\frac{3}{4}\right)$
2. (B)$\left(\frac{7}{2},\frac{9}{2}\right)$
3. (C)$\left(\frac{9}{2},-\frac{3}{4}\right)$
4. (D)$\left(\frac{7}{2},\frac{9}{4}\right)$

The distance of the point (5, 4) from the origin is

1. (A)41
2. (B)$\sqrt{41}$
3. (C)3
4. (D)9

Assertion (A) : The point (0, 4) lies on y – axis.
Reason (R) : The $x$-coordinate of a point, lying on y – axis, is zero.

1. (A)Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are correct but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

The distance of the point (3, 4) from the origin is

1. (A)25
2. (B)5
3. (C)7
4. (D)1

The distance between the points $A(-1,5)$ and $B(6,-2)$ is :

1. (A)$2\sqrt{7}$
2. (B)$7\sqrt{2}$
3. (C)49
4. (D)14

Assertion (A) : The distance of $P(a,b)$ from origin is $a^2+b^2$.
Reason (R) : The distance between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.

1. (A)Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true. Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

The distance between the points $A(5,-4)$ and $B(4,-5)$ is

1. (A)$\sqrt{2}$ units
2. (B)2 units
3. (C)1 unit
4. (D)$9\sqrt{2}$ units

If the distances of the point $P(x,y)$ from (1, 0) and (0, 1) are equal, then which of the following is true ?

1. (A)$x+y=0$
2. (B)$x=y+1$
3. (C)$y=x+1$
4. (D)$x=y$

The distance between the points $(2,-1)$ and $(-1,-5)$ is :

1. (A)15 units
2. (B)5 units
3. (C)25 units
4. (D)41 units

If $C(1,-1)$ is the mid-point of the line segment AB joining points $A(4,x)$ and $B(-2,4)$, then value of $x$ is :

1. (A)$5$
2. (B)$-5$
3. (C)$6$
4. (D)$-6$

The distance of the point $(4,5)$ from x-axis is :

1. (A)5
2. (B)4
3. (C)9
4. (D)1

The midpoint of the line segment joining the points $(-6,-4)$ and $(0,4)$ is :

1. (A)$(-6,0)$
2. (B)$(-3,0)$
3. (C)$(-6,8)$
4. (D)$(-6,4)$

The mid-point of the line segment AB joining $A(-2,8)$ and $B(-6,4)$ is :

1. (A)(2, 6)
2. (B)$(-4,12)$
3. (C)$(-4,6)$
4. (D)$(4,-6)$

AD is a median of $△ABC$ with vertices A$(5,-6)$, B$(6,4)$ and C$(0,0)$. Length AD is equal to :

1. (A)$\sqrt{68}$ units
2. (B)$2\sqrt{15}$ units
3. (C)$\sqrt{101}$ units
4. (D)10 units

If the distance between the points $(3,-5)$ and $(x,-5)$ is 15 units, then the values of $x$ are :

1. (A)$12,-18$
2. (B)$-12,18$
3. (C)18, 5
4. (D)$-9,-12$

The centre of a circle is at $(2,0)$. If one end of a diameter is at $(6,0)$, then the other end is at :

1. (A)(0, 0)
2. (B)(4, 0)
3. (C)$(-2,0)$
4. (D)$(-6,0)$

Point P divides the line segment joining the points A(4, $-5$) and B(1, 2) in the ratio 5:2. Co-ordinates of point P are

1. (A)$\left(\frac{5}{2},\frac{-3}{2}\right)$
2. (B)$\left(\frac{11}{7},0\right)$
3. (C)$\left(\frac{13}{7},0\right)$
4. (D)$\left(0,\frac{13}{7}\right)$

XOYZ is a rectangle with vertices X($-3$, 0), O(0, 0), Y(0, 4) and Z($x$, y). The length of its each diagonal is

1. (A)5 units
2. (B)$\sqrt{5}$ units
3. (C)$x^2+y^2$ units
4. (D)4 units

The distance between the points $(a\cos \theta ,-a\sin \theta )$ and $(a\sin \theta ,a\cos \theta )$ is

1. (A)a
2. (B)$a\sqrt{2}$
3. (C)0
4. (D)2a

Assertion (A) : The point which divides the line segment joining the points A (1, 2) and B($-1$, 1) internally in the ratio 1 : 2 is $\left(\frac{-1}{3},\frac{5}{3}\right)$
Reason (R) : The coordinates of the point which divides the line segment joining the points A ($x_1$, $y_1$) and B($x_2$, $y_2$) in the ratio $m_1:m_2$ are $\left(\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2},\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}\right)$

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

The fourth vertex D of a parallelogram ABCD whose three vertices are A($-2$, 3), B(6, 7) and C(8, 3) is :

1. (A)(0, 1)
2. (B)(0, $-1$)
3. (C)($-1$, 0)
4. (D)(1, 0)

Assertion (A) : Mid-point of a line segment divides the line segment in the ratio 1 : 1.
Reason (R) : The ratio in which the point ($-3$, k) divides the line segment joining the points ($-5$, 4) and ($-2$, 3) is 1 : 2.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

The distance between the points $(3,0)$ and $(0,-3)$ is

1. (A)$2\sqrt{3}$ units
2. (B)6 units
3. (C)3 units
4. (D)$3\sqrt{2}$ units

The distance between the points $\left(\frac{-5}{2},7\right)$ and $\left(\frac{-1}{2},7\right)$ is :

1. (A)3
2. (B)2
3. (C)4
4. (D)9

In what ratio does x-axis divide the line segment joining the points $A(2,-3)$ and $B(5,6)$ ?

1. (A)2 : 3
2. (B)2 : 1
3. (C)3 : 4
4. (D)1 : 2

y-axis divides the line segment joining the points $(-6,2)$ and $(2,-6)$ in the ratio :

1. (A)1 : 3
2. (B)3 : 2
3. (C)3 : 1
4. (D)2 : 3

The distance between the points A(0, 6) and B($-$ 6, 2) is :

1. (A)6 units
2. (B)$2\sqrt{6}$ units
3. (C)$2\sqrt{13}$ units
4. (D)$13\sqrt{2}$ units

The distance between the points (6, 2) and ($-$ 6, 2) is :

1. (A)$6\sqrt{2}$ units
2. (B)12 units
3. (C)$2\sqrt{6}$ units
4. (D)6 units

The distance of the point (5, 0) from the origin is

1. (A)0
2. (B)5
3. (C)$\sqrt{5}$
4. (D)$5^2$

If (2, 4) is the mid-point of the line-segment joining (6, 3) and (a, 5), then the value of a is

1. (A)2
2. (B)4
3. (C)$-4$
4. (D)$-2$

Distance of the point (6, 5) from the y-axis is

1. (A)6 units
2. (B)5 units
3. (C)$\sqrt{61}$ units
4. (D)0 unit

In what ratio, does x-axis divide the line segment joining the points A(3, 6) and B(–12, –3) ?

1. (A)1 : 2
2. (B)1 : 4
3. (C)4 : 1
4. (D)2 : 1

The distance between the points $(0,2\sqrt{5})$ and $(-2\sqrt{5},0)$ is

1. (A)$2\sqrt{10}$ units
2. (B)$4\sqrt{10}$ units
3. (C)$2\sqrt{20}$ units
4. (D)0

Assertion (A) : Point P(0, 2) is the point of intersection of y-axis with the line $3x+2y=4$.
Reason (R) : The distance of point P(0, 2) from x-axis is 2 units.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true but Reason (R) is false.
4. (D)Assertion (A) is false but Reason (R) is true.

The end-points of a diameter of a circle are (2, 4) and (–3, –1). The radius of the circle is

1. (A)$2\sqrt{5}$
2. (B)$\frac{5}{2}\sqrt{5}$
3. (C)$\frac{5}{2}\sqrt{2}$
4. (D)$5\sqrt{2}$

The coordinates of the vertex A of a rectangle ABCD whose three vertices are given as B(0, 0), C(3, 0) and D(0, 4) are :

1. (A)(4, 0)
2. (B)(0, 3)
3. (C)(3, 4)
4. (D)(4, 3)

The area of the triangle formed by the line $\frac{x}{a}+\frac{y}{b}=1$ with the coordinate axes is :

1. (A)$ab$
2. (B)$\frac{1}{2}ab$
3. (C)$\frac{1}{4}ab$
4. (D)$2ab$

The ratio in which the x-axis divides the line segment joining the points $(-2,3)$ and $(6,-7)$ is :

1. (A)1 : 3
2. (B)3 : 7
3. (C)7 : 3
4. (D)1 : 2

The distance of the point $(-1,7)$ from x-axis is :