CBSE Class 10 Maths (Basic) 2025 · Paper 430/6/1 · Question 38

Coordinate Geometry 4 marks Medium

Gurveer and Arushi built a robot that can paint a path as it moves on a graph paper. Some co-ordinate of points are marked on it. It starts from

(0, 0)

, moves to the points listed in order (in straight lines) and ends at

(0, 0)

. Arushi entered the points

P (8, 6), Q (12, 2), S (- 6, 6)

in order. The path drawn by robot is shown in the figure. Based on the above, answer the following questions.

Robot path on coordinate plane

iDetermine the distance $O P$ .[1]
ii $QS$ is represented by $2 x + 9 y = 42$ . Find the co-ordinates of the point where it intersects $y$ -axis.[1]
iii(a)Point $R (4.8, y)$ divides the line segment $O P$ in a certain ratio. Find the ratio. Hence, find the value of $y$ .[2]
iii(b)Using distance formula, show that $\frac{P Q}{O S} = \frac{2}{3}$ .[2]

Answer

(i)

O P = 10

units; (ii)

(0, \frac{14}{3})

; (iii)(a)

O R : R P = 3 : 2

and

y = \frac{18}{5} = 3.6

; (iii)(b)

P Q = 42

and

O S = 62

, so

\frac{P Q}{O S} = \frac{2}{3}

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