Question

In the given figure P(5, –3) and Q(3, y) are the points of trisection of the line segment joining A(7, –2) and B(1, –5). Then, y equals

Options

• 2

• 4

• –4

• `(-5)/2`

Answer 1

–4

Explanation:

From the given P(5, –3) one finds P divides AB in the ratio 1 : 2, so P is the first trisection point. 

Hence, Q is the other trisection point, dividing AB in the ratio 2 : 1.

Using the section formula for Q: 

`y = (2 xx (y_B) + 1 xx (y_A))/(2 + 1)`

= `(2 xx (-5) + 1 xx (-2))/3`

= `(-10 - 2)/3`

= `(-12)/3` 

= –4