Question

4 three points representing the corners of a rectangular garden are a (-7, 3), b (7, 3), and c (7, -3). part a graph the points representing the corners of the garden. explain how to find the coordinates of the fourth corner, point d. then graph and label that point. part b name two points that are reflections of each other across the x - axis. name two points that are reflections of each other across the y - axis. part c find the distance between two points that have the same y - coordinate.

Explanation:

Step1: Plot given points

Mark $A(-7, 3)$, $B(7, 3)$, $C(7, -3)$ on the grid:

• $A$: 7 left, 3 up from origin
• $B$: 7 right, 3 up from origin
• $C$: 7 right, 3 down from origin

Step2: Find point D (rectangle rule)

In a rectangle, opposite sides are equal and parallel. The $x$-coordinate of $D$ matches $A$ ($-7$), $y$-coordinate matches $C$ ($-3$). So $D(-7, -3)$. Plot $D$ on the grid.

Step3: Identify x-axis reflections

Reflect over x-axis: $(x,y)\to(x,-y)$. $B(7,3)$ and $C(7,-3)$ fit this rule.

Step4: Identify y-axis reflections

Reflect over y-axis: $(x,y)\to(-x,y)$. $A(-7,3)$ and $B(7,3)$ fit this rule.

Step5: Calculate same y-coordinate distance

Use points $A(-7,3)$ and $B(7,3)$. Distance formula for same $y$: $|x_2 - x_1|$
$\text{Distance} = |7 - (-7)| = |14| = 14$

Answer:

Part A

1. Plotting: Mark $A(-7, 3)$ (7 units left, 3 units up from the origin), $B(7, 3)$ (7 units right, 3 units up from the origin), and $C(7, -3)$ (7 units right, 3 units down from the origin) on the provided coordinate grid.
2. Finding $D$: In a rectangle, opposite vertices share matching $x$ or $y$ coordinates. $D$ must have the $x$-coordinate of $A$ ($-7$) and the $y$-coordinate of $C$ ($-3$), so $D(-7, -3)$. Plot this point (7 units left, 3 units down from the origin) and label it.

Part B

• Reflections across the x-axis: $B(7, 3)$ and $C(7, -3)$
• Reflections across the y-axis: $A(-7, 3)$ and $B(7, 3)$

Part C

14