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# How to Find the Length of a Median of a Triangle?

TopTriangle can be defined as Geometry which is composed of three line segments (sides) and three angles. Angle in triangle determines its shape. Triangles can be classified according to their size (angle). Triangles may be equilateral, isosceles, scalene triangle, oblique, right triangle (right-angled), acute, obtuse etc. type triangle. Total of internal angles of a triangle adds up to 180° (π radians). Let’s consider a triangle to determine how to find the length of a Median of a triangle?

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.