Question

A city grid of Anytown, USA is shown on the grid below. The fire department is represented by quadrilateral RSTU. Another fire department is opening in a different part of the city to maximize fire protection. The size of the new department's property must be congruent to the older department. Vertices A and B are plotted on the grid below to represent two vertices of the new fire department quadrilateral ABCD:
What could be the ordered pairs representing vertices C and D of quadrilateral ABCD so that the new fire department is congruent to the old fire department?

a. C(1,1) , D (4,1)
b. C (1,6) , D (4,6)
c. C (1,2) , D (4,2)
d. C (1,4) , D (4,4)

Answer 1

The shape of the fire departments are rectangles of coordinates 3 by 2.

There are only two possible 3 by 2 rectangles that we can draw, as shown in the picture:

I) C(1, 1), D(4, 1),                  or              II) C(1, 5), D(4, 5).

From the available choices, we see that the answer is only a.

Answer: a