# CBSE 2017 Board Paper

10th standard Math - AI Set 3 - Q14. Coordinate Geometry

#### Video Explanation

Let the ratio in which ($$frac{24}{11}$, y) divides the line segment PQ be m : n If a point k$x, y) divides a segment joining points A(x1, y1) and B (x2, y2) in the ratio m : n, then
x = $$frac {m{x}_{2}+n{x}_{1}} {m+n}$ and y = $\frac {m{y}_{2}+n{y}_{1}} {m+n}$ So, the x-coordinate $\frac{24}{11}$ = $\frac{m$3$ + n(2)}{m + n}))
Or $$frac{m}{n}$ = $\frac{2}{9}$ Therefore, m : n = 2 : 9 The ratio in which the point$$$frac{24}{11}$, y) divides the line segment PQ is 2 : 9. The y coordinate of the point = $\frac {m{y}_{2}+n{y}_{1}} {m+n}$ Or y = $\frac{$2(7$ + 9(-2)}{2+9}) = $\frac{14 - 18}{11}$ = -$\frac{4}{11}$