Class 10 Coordinate Geometry Mock Test (CBSE)

Topics in Coordinate Geometry

• Distance formula
• Section formula

Coordinate Geometry practice questions with answers

1. Q1Multiple choice·1 mark
   The distance of the point $P(-6, 8)$ from the origin is:

   1. (a)$6$
   2. (b)$8$
   3. (c)$10$
   4. (d)$14$
   Show answer and step marks

   1. Correct option: (c) $10$. Distance = $\sqrt{(-6)^2 + 8^2} = \sqrt{100} = 10$+1

   Answer: (c)
2. Q2Multiple choice·1 mark
   The ratio in which the line segment joining $A(-3, 10)$ and $B(6, -8)$ is divided by the point $(-1, 6)$ is:

   1. (a)$2:7$
   2. (b)$3:4$
   3. (c)$2:5$
   4. (d)$1:2$
   Show answer and step marks

   1. Correct option: (a) $2:7$. Let the ratio be $k:1$. Using the section formula for $x$-coordinate: $-1 = \frac{6k - 3}{k + 1} \implies -k - 1 = 6k - 3 \implies 7k = 2 \implies k = \frac{2}{7}$, so the ratio is $2:7$.+1

   Answer: (a)
3. Q3Multiple choice·1 mark
   The coordinates of the point which divides the line segment joining the points $(4, -3)$ and $(8, 5)$ in the ratio $3 : 1$ internally are:

   1. (a)$(7, 3)$
   2. (b)$(2, 5)$
   3. (c)$(3, 7)$
   4. (d)$(5, 2)$
   Show answer and step marks

   1. Correct option: (a) $(7, 3)$. Using section formula, $x = \frac{1(4) + 3(8)}{3+1} = 7$ and $y = \frac{1(-3) + 3(5)}{3+1} = 3$.+1

   Answer: (a)
4. Q4Assertion and reason·1 mark
   Assertion (A): The distance of the point $(-5, 12)$ from the origin is $13$ units. Reason (R): The distance of a point $(x, y)$ from the origin is $|x| + |y|$ 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.
   Show answer and step marks

   1. Correct option: (c) Assertion (A) is true but Reason (R) is false.+1

   Answer: (c)
5. Q5Short answer·2 marks
   The point $R$ divides the line segment joining $M(-2, 5)$ and $N(4, -1)$ internally in the ratio $1 : 2$. Find the coordinates of $R$.
   Show answer and step marks

   1. Using the section formula with $m = 1$, $n = 2$: $x = \frac{1 \times 4 + 2 \times (-2)}{1 + 2} = \frac{4 - 4}{3}$+1
   2. $x = 0$ and $y = \frac{1 \times (-1) + 2 \times 5}{3} = \frac{9}{3} = 3$, so $R = (0, 3)$+1

   Answer: $R = (0, 3)$
6. Q6Short answer·2 marks
   A bus travels in a straight line from town P, at the point $(-3, 2)$, to town Q, at the point $(9, 11)$, on a map where each unit represents 1 km. A relay tower R is built on this road so that the distance from P to R is twice the distance from R to Q. Find the coordinates of R.
   Show answer and step marks

   1. Take PR : RQ = 2 : 1, so R divides PQ internally in the ratio m : n = 2 : 1, and use $x=\frac{mx_2+nx_1}{m+n}$, $y=\frac{my_2+ny_1}{m+n}$ with $(x_1,y_1)=(-3,2)$ and $(x_2,y_2)=(9,11)$.+1
   2. Substitute: $x=\frac{2(9)+1(-3)}{2+1}=5$ and $y=\frac{2(11)+1(2)}{2+1}=8$, so R is $(5, 8)$.+1

   Answer: R $(5, 8)$

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