Question 1159255
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A very rough sketch of the four given points shows that it is not any of those shapes.<br>
Check the given coordinates and re-post the problem with the correct ones.<br>
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I could see that the point was supposed to be (7,-2) instead of (7,2) from the rough sketch....<br>
Here is a sketch pirated from the other tutor's response, with the corrected coordinates of that point.<br>
{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(4,6,.12),locate(4,6,A(4,6)),
circle(7,-2,.12),locate(7,-2,B(7,-2)),
circle(-1,-5,.12),locate(-1,-5,C(-1,-5)),
circle(-4,3,.12),locate(-4,3,D(-4,3)),
green(line(-4,3,4,6)),green(line(-4,3,-1,-5)),
green(line(-1,-5,7,-2)),green(line(7,-2,4,6)),
graph( 600, 600, -10, 10, -10, 10, 0)) }}}<br>
Now it looks very much like a square; and some simple calculations confirm that it is.<br>
From A to B and from D to C are both right 3 and down 8, so those segments have the same slope (-8/3) and the same length.<br>
And from D to A and from C to B are both right 8 and up 3, so those segments also have the same slope (3/8) and the same length.<br>
So all four sides of the quadrilateral have the same length, and the slopes of the two pairs of parallel sided are negative reciprocals; and that makes the quadrilateral a square.<br>