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Equal Angles Subtend Equal Sides

In a triangle...

Question

In a triangle ABC, side AB has the equation 2x + 3 y = 29 and the side AC has the equation x = 2y = 16, If the mid-points of BC is (5,6) then the equation of BC is ______________.

x-y=-1

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5x-2y=13

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x+y=11

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3x-4y=-9

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Solution

The correct option is C x+y=11
$L e t$
$C = (16 - 2 t, t)$
$B = (x_{1}, y_{1})$
$B y m i d p o i n t f o r m a l a$
$\frac{x_{1} + 16 - 2 t}{2} = 5 \Rightarrow x_{1} = 2 t - 6$
$y_{1} + t = 6 \times 2 \Rightarrow y_{1} = 12 - t$
$B = (2 t - 6, 12 - t)$
$B s a t i s f i e s 2 x + 3 y = 29$
$2 (2 t - 6) + 3 (12 - t) = 29$
$4 + - 12 + 36 - 3 + = 29$
$t = 4$
$C = (6, 5)$
$E q u a t i o n o f B C i s y - 6 = \frac{5 - 6}{6 - 5} (x - 5)$
$- 6 = - x + 5$
$x + y = 11$
$o p t i o n C i s c o r r e c t .$

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