Find out the length of median AD of a triangle whose vertices are P (-2, 6), Q (5, -3), and R (-7, 7).

Median PS is bisecting the side QR of the triangle. Slope of side QR will be calculated as follows:

Q (5, -3) = (x(a), y (a)) and R (-7, 7) = (x (b), y (b)) hence Slope

m = (y (b) – y (a)) / (x (b) – x (a)) = 7 – (- 3) / (- 7) – 5) = 7 + 3 / (- 7 – 5 ) = 10 / -12,

Half would be 5 / -6. Hence there will be change in 'x' of -6 and a change in 'y' of 5.

So Point 'S' will be S (5 - 6, -3 + 5) = S (-1, 2),

Let's use the distance formula to find the length of median PS. For this first we need to find the distance between point P (-2, 6) and S (-1, 2). Standard distance formula can be used to understand how to find the length of a median of a triangle?

This is given as

l = sqrt [(x (b)-x (a)

^{2}+ (y (b)-y (a)

^{2}],

= sqrt [(-2 – (-1)

^{2}+ (6 - 2)

^{2}],

= sqrt [(-2 +1)

^{2}+ (4)

^{2}],

= sqrt [(-1)

^{2}+ 16],

= sqrt (1 + 16),

= sqrt 17.