Question

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) and S(–6, 6) in order. The path drawn by robot is shown in the figure. Based on the above, answer the following questions:

(i) Determine the distance OP.

(ii) QS is represented by equation 2x + 9y = 42. Find the co-ordinates of the point where it intersects y-axis

(iii) (a) Point R(4.8, y) divides the line segment OP in a certain ratio, find the ratio. Hence, find the value of y.

OR

(iii) (b) Using distance formula, show that  \(\frac{PQ}{OS} = \frac{2}{3}\)

Answer 1

(i) From the gives diagram,

O(0, 0), P(8, 6)

\(\therefore\) Distance, OP = \(\sqrt {(8-0)^2 + (6-0)^2}\)  

\(= \sqrt {64+36}\) 

= 10 units 

(ii) Equation of line QS is 2x + 9y = 42

On y-axis, abscissa is zero

\(\therefore \) 2(0) + 9y = 42

⇒  9y = 42

y = \(\frac{14}{3}\) 

\(\therefore \) Required coordinate is \((0, \frac{14}{3})\)

(iii) (a) Let ‘R’ divides the line OP in ratio k : 1