Trapezoid wxyz has vertices w(−1, 2) , x(2, 2) , y(3, −1) , and z(−3, −1) . is the trapezoid an isosceles trapezoid?

Short No

Step-by-step explanation:

In order to be an isosceles trapezoid The distance between (2,2) and (3,-1) must be the same as the distance between (-1,2) and (-3,-1). Just by looking at it, you can tell they are not equal. But math never goes by looks. Let's actually find that distance.

d1 = sqrt( (y2 - y1)^2 + (x2 - x1)^2 )

y2 = 2    y1 = -1     x2 = 2       x1 = 3

d1 = sqrt(  (2 - - 1)^2 + (2 -3 ) ^2 )

d1 = sqrt(   (3^2)  +   (-1 )^2 )

d1 = sqrt( 9 + 1)  

d1 = sqrt(10)

============

d1 = sqrt( (y2 - y1)^2 + (x2 - x1)^2 )

y2 = 2

y1 = -1

x2 = - 1

x1 = -3

d2 = sqrt ( (2 - - 1)^2 + (-1 - - 3)^2 )

d2= sqrt(  ( 3^2) + (-1 + 3)^2 )

d2 = sqrt( 9 + 2^2)

d2 = sqrt( 9 + 4 )

d2 = sqrt(13)

=============≠

sqrt (10)  ≠ sqrt(13)

The trapezoid is not isosceles.

your answer would be 10x - 1