Question

Plans for a new apartment complex call for buildings directly across the fence fromeach other to be congruent. This computer printout shows Building A.If the vertices of Building B are located at (2x1,2y.), (2:02, 2y2), (2.23, 2y3), and(244, 244), will Building B be congruent to Building A?

Answer 1

The vertices of building B are the vertices of building A multiplied by a factor of 2.

If the buildings are congruent, then corresponding sides should have the same length.

If we take the side of building A that goes from (x1, y1) to (x1, y2), its length is |y2-y1|.

If we take the corresponding side for Building B that goes from (2*x1, 2*y1) to (2*x1, 2*y2), the length as distance between the vertices is now |2y2-2y1|=2*|y2-y1|.

Then, we have a corresponding side that is twice as long. Then, as we have at least one pair of corresponding sides that do not have the same length, we can conclude that the buildings are not congruent.

We can see that the transformation applied is a dilation.

To both buildings to be congruent, the transformation should have been a translation or rotation, but without a change in the scale.

Answer: No, because the transformation applied was a dilation.