Question

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

• A. $2x+y=16$
• B. $x+y=11$
• C. $2x-y=4$
• D. $x+y=-11$

Answer 1

The correct option is B $x+y=11$

$\frac{x_1+x_2}{2}=5\Rightarrow x_1+x_2=\mathrm{10.....}\left(1\right)and{y}_1+y_2=\mathrm{12.....}\left(2\right)$

$Point(x_1,y_1)$ lie on line AC

then

$x_1+2y_1=\mathrm{16...}\left(3\right)$

Similarly $2x_2+3y_2=\mathrm{29....}\left(4\right)$

$\Rightarrow 2(x_1+x_2)+4y_1+3y_2=32+292\times 10+4y_1+36-3y_1=61y_1=5\Rightarrow x_1=6\Rightarrow x_2=4\Rightarrow y_2=7$

now,

we take these two points and make equation,

$AC=x+y=11$