Question

A trapezoid is drawn on a grid with vertices at P (-5, 7), Q (-2, 7), R (2, 3), and S (-8, 3). Trapezoid UVWX will be drawn similar to Trapezoid PQRS with side WX corresponding to side RS. The point (1, 6) will be the location of vertex W and point (-4, 6) will be the location of point X. What will be the coordinates of vertex V? Show all your work or explain your reasoning.

Answer 1

WX corresponds to the long side of P Q R S
RS = 10 , WX = 5
so the dimensions of the new trapezoid are half the original.

x-distance P-S = 3
so x-distance U-X = 3/2 and the x-coordinate of U is -4+3/2 = -5/2
x-distance Q-R = 4
so x-distance W-V = 2 and the x-coordinate of V is 1-2 = -1

They probably intend for U-V to be above W-X,
in which case the y-coordinates of U and V would be
6+2 = 8

But it could just as well be below,
in which case the y-coordinates would 6 - 2 = 4

In summary,
U-V above X-W
U = (-5/2, 8) V = (-1,8) [ probably the intended answer ]

or

U-V below X-W
U = (-5/2, 4) V = (-1, 4) [ an equally valid answer ]

Similar figures do not have to be in the same orientation.

NOTE: Corresponding means similar in function or in character!

Answer 2

which one should I put though? the above or below?