Question

Point P(5, –3) is one of the two points of trisection of the line segment joining the points A(7, –2) and B(1, –5).

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Let P(5, –3) divides the line segment joining the points A(7, –2) and B(1, –5) in the ratio k : 1 internally.

By section formula, the coordinate of point P will be

`((k(1) + (1)(7))/(k + 1), (k(-5) + 1(-2))/(k + 1))`

i.e., `((k + 7)/(k + 1), (-5k - 2)/(k + 1))`

Now, (5, –3) = `((k + 7)/(k + 1), (-5k - 2)/(k + 1))`

⇒ `(k + 7)/(k + 1)` = 5

⇒ k + 7 = 5k + 5

⇒ – 4k = – 2

∴ k = `1/2`

So the point P divides the line segment AB in ratio 1 : 2.

Hence, point P in the point of trisection of AB.