SOLUTION: triangle DEF has vertices D(2,1)and E(7,1) and has an area of 15 square units plot possible point F on grid.

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Question 1026787: triangle DEF has vertices D(2,1)and E(7,1) and has an area of 15 square units plot possible point F on grid.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
First note that the vertices D and E are the endpoints of a segment that is parallel to the x-axis. (In fact the DE lies on the horizontal line y = 1.) The length of this segment is 7-2 = 5 units, which is also the base b of the triangle.
Now the area of a triangle is given by A+=+%281%2F2%29bh.
==> %281%2F2%29%2A5h=++15 as per given information
==> 5h = 30, or h = 6 units.
This means that as long as a point (x,y) has a distance of 6 units from the line y = 1, it is a third vertex F to a triangle with an area of 15 square units.
Thus, all points (x,7) and (x,-5) for arbitrary x value are all possible points for F.