Prove quadrilateral MATH, M (-4,-1) A(-3,2). T(3, 0), H(2, -3) is a rectangle

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

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