Q. 185.0( 2 Votes )

# 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 is (7, - 2) is equal to 2 units in magnitude.

Answer :

Given: A divides the join of P(-5, 1) and Q(3, 5) in the ratio k:1

To Find: Two values of K

A divides join of PQ in the ratio k:1 hence

Coordinates of A

Now, We have A , B (1, 5), and C(7, -2)

Now, The area of ABC is equal to the magnitude 2 (Given)

Area of ABC

14k - 66 = 4k + 4

14k - 66 = -4k - 4

10k = 70

18k = 62

Hence, k = 7 and

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