Answer:
Quadrilateral MATH is a rectangle
Step-by-step explanation:
Prove quadrilateral MATH, M (-4,-1) A(-3,2). T(3, 0), H(2, -3) is a rectangle
A rectangle is a quadrilateral whose opposite sides have the same lengths and are parallel.
We solve the above question using the formula below to find the length of its sides
= √(x2 - x1)² + (y2 - y1)² when we are given vertices(x1, y1) and (x2, y2)
For side MA
M (-4,-1) A(-3,2)
√(-3 - (-4))² + (2 - (-1))²
= √1² + 3²
= √1 + 9
= √10 units
For side AT
A(-3,2). T(3, 0)
√(3 - (-3))² + (0 - 2)²
= √6² + -2²
= √36 + 4
= √ 40 units
For side TH
T(3, 0), H(2, -3)
√(2 - 3)² + (-3 - 0)²
√-1² + -3²
= √1 + 9
= √10 units
For side MH
M (-4,-1) H(2, -3)
√(2 - (-4))² + (-3 - (-1))²
= √6² + 2²
= √36 + 4
= √40 units
From the above calculation, we can see that
Side MA = Side TH = √10 units
Side AT = Side MH = √40 units
Opposite sides are parallel to each other, hence quadrilateral MATH is a rectangle
