Question

Find the equation of the median through the vertex A of $\Delta ABC$ whose vertices are A(2, 5), B(-4, 9) and C(-2, -1).

• A. x - 5y + 23 = 0
• B. x + 5y + 23 = 0
• C. x + 5y - 23 = 0
• D. x - 5y - 23 = 0

Answer 1

The correct option is A x - 5y + 23 = 0

Let AD be median on BC



The coordinates of point D are

$=(\frac{-4-2}{2},\frac{9-1}{2})$

= (-3, 4)

The equation of median AD on BC is

$\Rightarrow y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$\Rightarrow y-5=\frac{4-5}{-3-2}(x-2)$

$\Rightarrow y-5=\frac{-1}{-5}(x-2)$

$\Rightarrow 5y-25=x-2$

$\Rightarrow 5y-25-x+2=0$

$\Rightarrow -x+5y-23=0$

$\Rightarrow -(x-5y+23)=0$

$\therefore x-5y+23=0$

Hence, option a is correct.