Question

performance task
for each part a through c, answer the question and include justifications.
jada works as an urban planner for a city. she is reviewing the plans for a shopping center shown in the diagram. she is examining if the locations of the building can be changed to make better use of the land.
part a
jada wants to increase the size of a parking lot, so she wants to know if building 2 can be reflected across the y - axis without intersecting any of the other buildings in the diagram. is this possible? explain.
part b
can building 2 be rotated 90° clockwise around the origin without intersecting with any of the other buildings? explain.
part c
jada decides she wants to move building 1 so that its sides touch the sides of buildings 2 and 4, but do not overlap these buildings. what transformation can she perform? what are the new coordinates of building 1?
unit reflect
how can you use transformations to describe the congruence of two figures?

Explanation:

Step1: Analyze Part A

When reflecting a point $(x,y)$ across the $y -$axis, the new point is $(-x,y)$. Building 2 is in the first - quadrant. When reflected across the $y -$axis, its new position will intersect with Building 4 which is in the second - quadrant. So the answer to Part A is no.

Step2: Analyze Part B

The rule for a $90^{\circ}$ clockwise rotation around the origin is $(x,y)\to(y, - x)$. By visual inspection of the grid, when Building 2 is rotated $90^{\circ}$ clockwise around the origin, it will not intersect with any other buildings. So the answer is yes.

Step3: Analyze Part C

To move Building 1 so that its sides touch the sides of Buildings 2 and 4 without overlapping, we can translate Building 1. If we translate Building 1 up and to the right. Let's assume Building 1 has vertices with coordinates (for example, if the bottom - left vertex is $(x_1,y_1)$ etc.). To touch Building 2 and 4, we can translate Building 1 6 units to the right and 4 units up. If the original bottom - left vertex of Building 1 is $(- 8,-8)$, the new bottom - left vertex will be $(-8 + 6,-8 + 4)=(-2,-4)$. The other vertices can be adjusted accordingly based on the shape of Building 1.

Answer:

Part A: No. When Building 2 is reflected across the y - axis, it will intersect with Building 4.
Part B: Yes. When rotated 90° clockwise around the origin, it will not intersect with other buildings.
Part C: Translation. For example, if the original bottom - left vertex of Building 1 is $(-8,-8)$, after translating 6 units to the right and 4 units up, the new bottom - left vertex is $(-2,-4)$ and other vertices are adjusted based on the shape of the building.