Given that <span>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 to represent
two vertices of the new fire department quadrilateral ABCD.
Map of Anytown; the line y equals 7 is Main Road; the line y equals 3 is
Rose Lane; the line y equals negative 1 is Crystal Avenue; the line x
equals negative 4 is Brick Street; the diagonal line is Dogwood Drive;
Old Fire Department forms quadrilateral with ordered pairs R at negative
4, 7, S at negative 1, 7; T at negative 1, 3; U at negative 4, 3; A is
at 4, negative 1 and B is at 1, negative 1
Recall that t</span><span>wo shapes are said to be congruent if the lengths of the sides and the angles are the same.
For quadrilateral RSTU to be congruent to quadrilateral ABCD, then RS = AB, RU = AD, ST = BC and TU = CD
Also, the figure ABCD is a result of a rigid body translation of the figure RSTU.
Given that R is at point (-4, 7) and A is at point (4, -1), also given that S is at point (-1, 7) and B is at point (1, -1).
It can be seen that points AB is a result of refrecting points RS across the y-axis and then shifting the resulting points down by 8 units.
Thus, given point T as (-1, 3) and point U as (-4, 3), refrection of points T and U across the y-axis will result in points (1, 3) and (4, 3), then shifting the resulting points down by 8 units will result to points (1, -5) and (4, -5)
Therefore, the ordered pairs representing vertices C and D of
quadrilateral ABCD so that the new fire department is congruent to the
old fire department are C(1, -5) and D(4, -5).</span>
