Question

If A (-4,6), B(2,-2) and C(2,5) are the vertices of a triangle ABC, find the length of the median through A and coordinates of centroid of the triangle.

Answer 1

Answer:

Midpoint of D =22+1,2−5−2=(23,2−7)

Equation of BD is m=23+2−27−3=7−13(y−3)=7−13(x+2)7y−21=−13x−2613x+7y+5=0

∴ Median BE is 13x+7y+5=0

Answer 2

DEAR MATE❣️:

Let AD be the median through A.

Median AD of the triangle will divide the side BC in two equal parts. So D is the midpoint of side BC.

The coordinates of D are given by:

$\binom{2 + 2 , \:- 2 + 5}{2 \: \: \: \: \: \: \: \: 2} = (2 + \frac{3}{2} )$

Thus, using the distance formula,

The length of median through A= Length of AD

$= \sqrt{ ({2 + 4}^{2} ) + ( \frac{3}{2} - {6}^{2} ) }$

Now, simplify this to get required length of median.

HOPE IT'S CLARIFIES U❣️