Question

In AABC, A(3, 5), B(7, 8) and C(1, -10). Find the equation of the median through A.​

Answer 1

Answer:

Median through A bisects the opposite side into two equal parts.

Let it bisect the opposite BC at D.

BD=CD

B(7 , 8)

C(1 , -10)

mid point of BC is

$(\frac{7 + 1}{2} \: \: \frac{8 - 10}{2} )$

D(4 , -1)

Slope of line AD is

$\frac{y2 - y1}{x2 - x1}$

$\frac{4 - 3}{ - 1 - 5} \\m = - \frac{1}{6}$

Equation of line AD is

$(y - y1) = m(x - x1) \\ (y - 4) = \frac{ - 1}{6} (x + 1) \\ 6y - 24 = - x - 1 \\ x + 6y - 23 = 0$

The equation of the median of tge given triangle is x + 6y - 23 = 0

KINDLY MARK AS BRAINLIEST.....