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

Explanation:

Step1: Recall reflection rule

When a point $(x,y)$ is reflected across the $y - axis$, the new point is $(-x,y)$. For Building 2, its right - most point is at $(5,0)$ and left - most at $(3,0)$ and top - most at $(5,2)$ and bottom - most at $(3,2)$. After reflection across the $y - axis$, the new right - most point will be at $(- 5,0)$ and left - most at $(-3,0)$ and top - most at $(-5,2)$ and bottom - most at $(-3,2)$.

Step2: Check for intersection

Building 4 is between $x=-4$ and $x = - 2$ and $y=-2$ and $y = 2$. Building 3 is at $x = 0$ to $x = 4$ and $y = 6$ to $y = 8$. Building 1 is at $x=-8$ to $x=-4$ and $y=-8$ to $y=-4$. The reflected Building 2 ($-5\leq x\leq - 3$ and $0\leq y\leq2$) will not intersect with Building 3 (since $y$ values are different) and will not intersect with Building 1 (different $y$ values) and will not intersect with Building 4 (different $y$ values).

Answer:

Yes, it is possible. When Building 2 is reflected across the $y - axis$, its new $x$ and $y$ coordinates place it in an area where it does not intersect with any of the other buildings in the diagram as the $y$ - value ranges of the other buildings are different from that of the reflected Building 2.