A city grid of Anytown, USA is shown on the grid below. The fire department is represented by quadrilateral RSTU. Another fire d
epartment 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)
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.
