Question

If A(5,-1), B(-3,-2) and C(-1,8) are the vertices of a triangle ABC, find the length of the median through A and the coordinates of the centroid.

(PLZ EXPLAIN STEPWISE)

Answer 1

Answer is below in the in the pic

Answer 2

Answer:

The length of the median is $\sqrt{65}$ units. The centroid is $(\frac{1}{3}},{\frac{5}{3})$.

Step-by-step explanation:

The vertices of the triangle are A(5,-1), B(-3,-2) and C(-1,8).

It is given that a median through A. Median divides the opposite side in two equal parts. It means the median divides BC at its midpoint.

$D=\text{Midpoint of BC}=(\frac{-3-1}{2},\frac{-2+8}{2})=(-2,3)$

The length of median is

$AD=\sqrt{(5-(-2))^2+(-1-3)^2}=\sqrt{49+16}=\sqrt{65}$

Therefore the length of the median is $\sqrt{65}$ units.

The formula of centroid is

$C=(\frac{x_1+x_2+x_3}{3}},{\frac{y_1+y_2+y_3}{3})$

$C=(\frac{5-3-1}{3}},{\frac{-1-2+8}{3})$

$C=(\frac{1}{3}},{\frac{5}{3})$

Therefore the centroid is $(\frac{1}{3}},{\frac{5}{3})$.