Question

ii) Find the ratio in which point A(6, 7) divides the segment joining P(8,9) and Q(1,2) by filling the boxes.
Let P(xj,y); Q(x2,y) and A(x,y) be the given points.

Answer 1

Step-by-step explanation:

Answer

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Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then 

(x,y)=(m+nmx2+nx1,m+nmy2+ny1)

Let the ratio be x: 1. 

Using the section formula,

k=x+11x+1×8

⇒kx+k=x+8..(1)

Also,7=x+12x+9

⇒7x+7=2x+9

⇒5x=2

⇒x=52

So, the required ratio is 2 : 5. 

Putting this value of x in (1) we get

k(52+1)=52+8

⇒57k=542