Question

Given the coordinates of a triangle, A (-3,-4), B (5,-2), C (-5,6)
1. Find the midpoints of each side of the triangle
2. Find the distances of each of the medians of the triangle (the line segment joining the vertex of a triangle and the midpoint of the opposite side)

Answer 1

The midpoint of each line segment is the average of its endpoints.
M(AB) = (A+B)/2 = ((-3+5)/2, (-4-2)/2) = (1,-3)
Do the others in the same way.

Then use your distance formula to find the length of each median.
The length of the median from C to M(AB) is
√((1+5)^2 + (-3-6)^2) = √(36+81) = √117

Answer 2

!. A(-3, -4), M(x, y), B(5, -2).
x + 3 = (5+3)/2,
X = 1.
y+4 = (-2+4)/2,
Y = -3.

B(5, -2), M(x, y), C(-5, 6).
x-5 = (-5-5)/2,
X = 0.
y+2 = (6+ 2)/2,
Y = 2.

A(-3, -4), M(x, y), C(-5, 6).

Answer 3

2. M(1, -3), C(-5, 6).
(MC)^2 = (-5-1)^2 + (6+3) = 36 + 81 = 117,
MC = 10.8.

M(0, 2), A(-3, -4),
(MA)^2 = (-3-0)^2 + (-4-2)^2 = 9 + 36 = 45.
MA = 6.7.

M(x, y), B(5, -2).