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Question: Let A(2, 4), B(–3, –8) and C(x, y) are three points such that ŠACB is a right angle and the area of ...

Let A(2, 4), B(–3, –8) and C(x, y) are three points such that ŠACB is a right angle and the area of DABC = (41/2) units. The number of such points C is

A

0

B

2

C

4

D

Infinite

Answer

4

Explanation

Solution

AB = (5)2+(4+8)2\sqrt{(5)^{2} + (4 + 8)^{2}}= 13

2r = 13 Ž r = 13/2

DABC = 12\frac{1}{2} × 13 × h = 412\frac{41}{2} Ž h = 4113=3213\frac{41}{13} = 3\frac{2}{13}