Four points A (6, 3), B(-3, 5), C(4, -2) and D(x, 3x) are given in such a way that , find x.

Question

Four points A (6, 3), B(-3, 5), C(4, -2) and D(x, 3x) are given in such a way that  , find x.

Philoid · Accepted Answer

Key points to solve the problem:

• Idea of distance formula- Distance between two points P(x₁,y₁) and Q(x₂,y₂) is given by- PQ =

• Area of a ΔPQR – Let P(x_1,y₁) , Q(x₂,y₂) and R(x₃,y₃) be the 3 vertices of ΔPQR.

Ar(ΔPQR) =

Given, coordinates of triangle as shown in figure.

Also,

ar(ΔDBC) =

=

Similarly, ar(ΔABC) =

=

∴

⇒ 24.5 = 28x – 14

⇒ 28x = 38.5

⇒ x = 38.5/28 = 1.375