Asked by amber
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?
Answers
Answered by
Steve
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.
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.
Answered by
Anonymous
Which is the best classification for RSTU?
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