Question

The coordinates of triangle MNP and triangle QRS are shown in the table.

Triangle MNP
Triangle QRS
M(2, 5) N(6, 4) P(6, 8)
Q(–2, -5) R(–6, -4) S(–6, -8)

Which BEST describes the relationship, in terms of congruency, between triangle MNP and triangle QRS?

Answer 1

Using translation concepts, it is found that the triangles are congruent, as triangle QRS is the result triangle after a 180º rotation about the origin of triangle MNP.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.

From the vertices of the triangles MNP and QRS, the following transformation was applied:

(x,y) -> (-x,-y).

Which is a 180º rotation about the origin, that is, triangle QRS is the result triangle after a 180º rotation about the origin of triangle MNP.

Rotations do not change the side lengths, only the orientation of the triangle, hence the triangles QRS and MNP are congruent.

More can be learned about translation concepts at https://brainly.com/question/4521517

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