a) The coordinates for T and H such that quadrillateral MATH is a rectangle are T(x, y) = (2, - 2) and H(x, y) = (5, - 4).
b) The quadrilateral MATH is a rectangle.
How to create and analyze quadrillateral on a Cartesian plane
Quadrilaterals are figures with four sides and whose internal angles sums a total of 360 degrees. A quadrilateral is a rectangle when each pair of opposite sides are parallel and have the same length to each others, each of the four angles are right angles and each pair of perpendicular sides.
a) Vectorially speaking, we can construct a rectangle by using the following definitions:
M(x, y) = (a, b), A(x, y) = (c, d), T(x, y) = (a, d), H(x, y) = (c, b)
If we know that a = 2, b = - 4, c = 5, d = - 2, then the points T and H are described below:
T(x, y) = (2, - 2), H(x, y) = (5, - 4)
The coordinates for T and H such that quadrillateral MATH is a rectangle are T(x, y) = (2, - 2) and H(x, y) = (5, - 4).
b) To prove that quadrilateral MATH, we need to prove that:
MT = HA
(2, - 2) - (2, - 4) = (5, - 2) - (5, - 4)
(0, 2) = (0, 2)
TA = MH
(5, - 2) - (2, - 2) = (5, - 4) - (2, - 4)
(3, 0) = (3, 0)
MT • TA = 0
(0, 2) • (3, 0) = 0 · 3 + 2 · 0 = 0
MH • HA = 0
(3, 0) • (0, 2) = 3 · 0 + 0 · 2 = 0
Therefore, the quadrilateral MATH is a rectangle.
To learn more on quadrilaterals: https://brainly.com/question/13805601
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