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 Δ ABC where B is (1, 5) and C (7, - 2) is equal to 2 units.

Given: Area ΔABC = 2 units

To find: The value of k.

Formula Used:

section formula:

If point P (x, y) divides the line segment A (x₁, y₁) and B(x₂,y₂)

Then the coordinates of P are:

Area of the triangle having vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃)
= 1/2 |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |

Explanation:

coordinates A can be given by using section formula for internal division,

A

and B (1,5), C (7, −2)

Area of ∆ABC

But Area ∆ABC = 2

Solving above we get,

Taking positive sign, 14k – 66 = 4k + 4

10k = 70

k = 7

Taking negative sign, we get,

14k − 66 = −4k − 4

18k = 62