Question

Four lines are drawn on a coordinate plane to form trapezoid WXYZ.

A coordinate grid with 4 lines. Line X W is drawn with point W at (negative 4, 1) and passes through (0, 2) with and (3, 3). Line Y X is drawn with point Y at (3, 0) and passes through (0, 3). Line Z W is drawn with point Z at (0, negative 3) and point W at (negative 4, 1). LIne Z Y is drawn with point Y at (3, 0) and point Z at (0, negative 3).

Which statements are true about the lines? Select three options.

Line WZ has the same slope as line XY.
Line YX has a greater slope than line ZY.
Line XW has a lesser slope than line YZ.
Line ZW has the same y-intercept as line YZ.
Line XY has a lesser y-intercept than line XW.

Answer 1

Answer:
- Line WZ has the same slope as line XY — True.
- Line XW has a lesser slope than line YZ — True.
- Line ZW has the same y-intercept as line YZ — True.

Work (using W = (−4,1), X = (0,3), Y = (3,0), Z = (0,−3)):
- slope WZ = (−3−1)/(0−(−4)) = −4/4 = −1. slope XY = (0−3)/(3−0) = −3/3 = −1 → same slope.
- slope YZ = (0−(−3))/(3−0) = 3/3 = 1. slope XW = (3−1)/(0−(−4)) = 2/4 = 1/2 → XW < YZ.
- y-intercept of ZW: using y = −x + b and W: 1 = −(−4)+b → b = −3. YZ through Z(0,−3) has intercept −3 → same intercept.

The other two statements are false.