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