What is the length of the midsegment of the trapezoid made by the vertices a(0, 5), b(3, 3), c(5, -2) and d(-1, 2). show equations and all work that leads to your answer.

Step-by-step explanation:

First we have to identify the parallel sides of the trapezium.

We know that the slopes are equal for parallel lines.

Slope of (x₁,y₁) and (x₂,y₂) is given by

Slope of AB:

Slope of BC:

Slope of CD:

Slope of DA:

We see that the slopes of AB and CD are equal, so, AB and CD are the parallel sides.

The length of the midsegment = (1/2)*(length of base1 + length of base2 )

Length of the bases can be calculated using distance formula,

AB =

CD =

Length of the midsegment = (1/2) (√13 + 2√13) =3√13/2

i don't think there is enough