Question

The point A divides the join of P (−5, 1) and Q(3, 5) in the ratio k:1. Find the two values of k for which the area of ΔABC where B is (1, 5) and C(7, −2) is equal to 2 units.

Answer 1

GIVEN: point A divides the line segment joining P (−5, 1) and Q (3, −5) in the ratio k: 1

Coordinates of point B (1, 5) and C (7, −2)

TO FIND: The value of k

PROOF: point A divides the line segment joining P (−5, 1) and Q (3, −5) in the ratio k: 1

So the coordinates of A are

We know area of triangle formed by three points is given by $∆=\frac{1}{2}\left|\left(x_1{y}_2+x_2{y}_3+x_3{y}_1\right)-\left(x_2{y}_1+x_3{y}_2+x_1{y}_3\right)\right|$

Now Area of ΔABC= 2 sq units.

Taking three points A , B (1, 5) and C (7, −2)

Hence