Question

Given the vertices of a triangle ABC below, find the midpoint and length of the midsegment. Give your length in simplified radical form.

Answer 1

Midpoint of AC = (-1, 1)

Midpoint of BC = (1, -2)

Length of the midsegment =
`√(13)`

Explanation:

Vertices of a triangle ABC are A(0, 5), B(4, -1) and C(-2, -3).

Midpoint of segment AC =
`(x_1+x_2)/(2),(y_1+y_2)/(2)`

=
`((0-2)/(2),(5-3)/(2))`

= (-1, 1)

Midpoint of BC =
`((4-2)/(2),(-1-3)/(2))`

=
`(1,-2)`

Length of the mid segment =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

=
`√((-1-1)^2+(-2-1)^2)`

=
`√(4+9)`

=
`√(13)`