Quadrilateral MATH has coordinates M A T H (1,1), ( 2,5), (3,5), and (6,1). Prove that quadrilateral MATH is a rhombus, but not a square.

Question

This is the question on paper.

Answer 1

 

AT has length 3-(-2)=5 and MH has length 6-1=5.

AM is the hypotenuse of a triangle where AM=√((1-(-2))²+(5-1)²)=√(3²+4²)=5.

Similarly, HT=√((6-3)²+(5-1)²)=√(3²+4²)=5.

So all sides of the quadrilateral are equal—a rhombus (with AT parallel to MH and AM parallel to TH).

But AT and MH are horizontal, while AM and TH are not vertical, because their x-coordinates are not the same. So MATH is a rhombus but not a square.