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

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )

113.1

step-by-step explanation:

v=4

3πr3=4

3·π·33≈113.09734