Question 1183287: Quadrilateral MATH includes the points M(2,-4) and A(5,-2).
Part A: Find coordinates for T and H such that quadrilateral MATH is a rectangle.
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821)   (Show Source):
You can put this solution on YOUR website!
The line segment,  , defined by the two given points, given a standard naming convention for the vertices of a quadrilateral, must perforce be one side of the desired rectangle. Since segments  and  must, by the definition of a rectangle, be perpendicular to , the first step is to calculate the slope of the line that contains .
}{5\,-\,2}\ =\ \frac{2}{3})
Perpendicular lines have negative reciprocal slopes, consequently the lines that contain and must have slope  .
Using the Point-Slope Form of an equation of a line, we write the equation for the line containing thus:
\ =\ -\frac{3}{2}(x\,-\,5))
Likewise, the line containing :
\ =\ -\frac{3}{2}(x\,-\,2))
Constructing those two lines gives:
 .
Now choose any value you like, except  which would lead us to a degenerate rectangle, and find the value of the function \ =\ -\frac{3}{2}x\,-\,1) at that selected value. I chose  just because it will simplify the arithmetic.
\ =\ -\frac{3}{2}(0)\,-\,1\ =\ -1)
Hence, ) is a point on the line  . This is a suitable point  . And a line perpendicular to through would create a suitable fourth side to the desired rectangle.
Finding an equation of the line that contains the segment that comprises the fourth side and then solving the 2X2 system of this fourth side and  to find the coordinates of point  are left as an exercise for the student.
 .
John
My calculator said it, I believe it, that settles it
From
I > Ø
Answer by ikleyn(52866)  (Show Source):
You can put this solution on YOUR website! .
Quadrilateral MATH includes the points M(2,-4) and A(5,-2).
Part A: Find coordinates for T and H such that quadrilateral MATH is a rectangle.
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There are INFINITELY MANY such points T and H.
Under these condition, IT IS NOT POSSIBLE to select and to determine a unique pair of points T and H.
So, I'd say that the problem MAKES no SENSE, as it is worded, printed, posted and presented in this post.
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