Question 1011466: Square QRST has vertices Q(2,8),R(-4,8),S(-4,2),and T(2,2).Triangle QTU shares 2 vertices with square QRST.Whichordered pair describes point U if the area of the triangle QTU is the same as the area of square QRST?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The square has sides parallel to the x-axis,
and sides parallel to the y-axis such as  on the line  .
The length of the side of the square
is the distance
 .
If we consider to be the base of square and triangle,
the area of the square is  ,
and the area of the triangle is
 .
We want  --> --> --> .
So  is a point at a distance of  units from line containing segment base .
It could be anywhere on line  <--> , or
on line  --> .
So without any other specification in the problem,
an infinite number of ordered pairs describe point ,
and an infinite number of possible triangles.
I will draw just the lines  and  ,
and a few of the triangles.
If we want to make triangle  isosceles (don't we all love symmetrical shapes?),
and we want named counterclockwise, as square  was,
then is  .
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