Question

quadrilateral RSTU has vertices R(-6,-3), S(3,3), and T(4,-1). what are the coordinates of vertex U if RSTU is a parallelogram?

Answer 1

we need the sides in pairs to have equal slope and equal length.

Slopes:
RS=2/3
ST=-4
So, we need TU to have slope 2/3 and UR to have slope -4.

Since UR goes through (-6,-3), its equation is

y+3 = -4(x+6)
and TU is
y+1 = 2/3 (x-4)

These lines intersect at U=(-5,-7)

Check the lengths:
RS = √((3+6)^2+(3+3)^2) = √117
ST = √((4-3)^2+(-1-3)^2) = √17
TU = √((-5-4)^2+(-7+1)^2) = √117
UR = √((-5+6)^2+(-7+3)^2) = √17

So, it looks like we're OK.

Answer 2

Which is the best classification for RSTU?