First slide

Equation of line in Straight lines

Question

ABC is an isosceles triangle. If the coordinates of the base are $B (1, 3) and C (- 2, 7)$ ,the coordinates of vertex A can be

Moderate

A

(1,6)
B

$(- \frac{1}{2}, 5)$
C

$(\frac{5}{6}, 6)$
D

None of these

Solution

Let the vertex of triangle be $A (x, y)$ ABC is an isosceles triangle. Therefore,
${(x - 1)}^{2} + {(y - 3)}^{2} = {(x + 2)}^{2} + {(y - 7)}^{2}$
or
$6 x - 8 y + 43 = 0$
Thus, any point lying on this line can be the vertex A except the midpoint $(- \frac{1}{2}, 5)$ of BC. Hence, vertex Ais $(\frac{5}{6}, 6)$ .

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