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Question

If A(x,0), B(-4,6), and C(14, -2) form an isosceles triangle with AB=AC, then x=
37/9
31/9
-3
-4

A

37/9

B

31/9

C

-3

D

-4

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Solution

Verified by Toppr

AB = AC or $A B^{2} = A C^{2}$
or ${(x + 4)}^{2} + {(0 - 6)}^{2} = {(x - 14)}^{2} + {(0 + 2)}^{2}$
or $x^{2} + 8 x + 16 + 36 = x^{2} - 28 x + 196 + 4$
or 36x = 148 or x = $\frac{148}{36} = \frac{37}{9}$

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