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in Mathematics by (76.3k points)

A triangle ABC, right angled at A, has points A and B as (2, 3) and (0, –1) respectively. If BC = 5 units, then the point C is

(1) (–4, 2) 

(2) (4, 2)

(3) (3, –3) 

(4) (0, –4)

1 Answer

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Best answer

(2) (4, 2)

Explanation

Let the coordinates of C be (x, y). Then

BC = 5

x2 + (y + 1)2 = 52    .....(1)

Since AB ^ AC, therefore 

2y –6 = –x + 2 x = –2y + 8 ..... (2)

from (1) and (2)(–2y +8)2 + (y +1)2 = 52

5y2 –30y + 40 = 0

y2 –6y + 8 = 0 , y = 2, 4

Putting y = 2 and y = 4 in (2), we get x = 4, x =0 respectively Hence, the coordinates of C are (4, 2) or (0,4)

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