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:
• The 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(x1,y1) , Q(x2,y2) and R(x3,y3) be the 3 vertices of ΔPQR.
Ar(ΔPQR) =
Given, coordinates of the triangle as shown in the figure.
Also,
ar(ΔDBC) =
=
Similarly, ar(ΔABC)
∴
⇒ 24.5 = 28x – 14
⇒ 28x = 38.5
⇒ x = 38.5/28 = 1.375 …ans