Question

Find the lengths of the medians AD and BE of triangle ABC whose vertices are A(7,-3) B(5,3) and C(3,-1).

Answer 1

Hii friend,

Since D and E are the midpoints of BC and AC respectively.

So their coordinates are,

D(X1+X2/2) , (Y1+Y2/2)

D[(5+3/2) , (3+(-1)/2]

and,

E(X1+X2/2 ) , (Y1+Y2/2)

E(7+3/2), ( -3-1/2)]

Therefore,

D(4,1) and E(5,-2)

Therefore,

Using distance formula,

AD = under root (7-4)² + (-3-1)² = ✓3² + (-4)²

= ✓9+16 = ✓25 = 5 units.

And,

BE = under root (5-5)² + (-2-3)² = ✓0+(-5)² = ✓25 = 5 units..

HOPE IT WILL HELP U.. :-)