Question

nikki drew a rectangle with a perimeter of 18 units on a coordinate grid. two of the vertices were (4, -3) and (-1, -3). what could be the coordinates of the other two vertices of the rectangle? (4, 12) and (-1, 12) (-1, 1) and (4, 1) (4, 6) and (-1, 6) (4, 7) and (-1, 7)

Explanation:

Step1: Calculate side - length from given vertices

The two given vertices $(4, - 3)$ and $(-1,-3)$ have the same $y$ - coordinate. The length of this side is $|4-(-1)|=5$ units.

Step2: Calculate the other side - length using perimeter

The perimeter of a rectangle is $P = 2(l + w)$. Given $P = 18$ and $l = 5$, then $18=2(5 + w)$. Solving for $w$:
\[

$$\begin{align*} 18&=2(5 + w)\\ 9&=5 + w\\ w&=4 \end{align*}$$

\]

Step3: Find the other vertices

Since the $y$ - coordinate of the given vertices is $-3$, and the other side - length is $4$ units, the $y$ - coordinate of the other two vertices should be $-3 + 4=1$. The $x$ - coordinates remain the same as the given vertices for the corresponding sides of the rectangle. So the other two vertices are $(-1,1)$ and $(4,1)$.

Answer:

$(-1,1)$ and $(4,1)$