Acity 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(−7, 3), d(−7, 5)
b. c(2, 3), d(2, 5)
c. c(−2, 3), d(−2, 5)
d. c(0, 3), d(0, 5)

option d. C (0,3), D (0,5).

Justification:

1) The x - coordinates of the vertices A and B are shown in the diagrama, They are both - 4, so the new vertices C and D must be in a line parallel to y = - 4.

2) The y-coordinates of the  vertices A and B are also shown in the diagrama. They  are equal to 3 and 5 respectively.

3) We can see that the new points C and D must be over a parallel line to y = - 4 and that their distance to the points A and B has to be the same distance of the point R and S to U and T.

That distance is 4, so the line may be y = - 7 or y = 0.

4) If the line is y = 7 the points C and D would have coordinates (-7,3) and (-7,5), but this points are not among the options.

5) If the line is y = 0 the points C and D would have coordinates (0, 3) and (0,5), which is precisely the points of the option d. That is the answer.