Question

Plans for a new shopping center call for buildings directly across the sidewalk from each other to be congruent. This computer printout shows a clothing store.

If the vertices of a home improvement store are located at (−x1,y1), (−x2,y2), (−x3,y3), and (−x4,y4), will the home improvement store be congruent to the clothing store?

Answer 1

Answer: yes, because the home improvement store is a reflection of the clothing store.

Explanation:

Imagine math!!!

Answer 2

Yes, both stores will be congruent

Explanation:

The given coordinates of the vertices of the home improvement store are;

(-x₁, y₁), (-x₂, y₂), (-x₃, y₃) and (-x₄, y₄)

The coordinates of the vertices of the clothing store are;

(x₁, y₁), (x₂, y₂), (x₃, y₃) and (x₄, y₄)

Therefore, the coordinates of the vertices of the home improvement store, corresponds to the coordinates of the vertices of the image of the reflection of the clothing store across the sidewalk (which is the y-axis)

A reflection of (x, y) across the y-axis gives (-x, y)

Given that a reflection is a rigid transformation, the dimensions (lengths and angles between corresponding sides) of the home improvement store and the clothing store are equal, therefore, the home improvement store will be congruent to the clothing store.