Question

1. maintain accuracy a certain rectangle has a perimeter of 10 units and an area of 6 square units. two of the vertices have coordinates (1, 7) and (1, 4). determine the coordinates of the two missing vertices.

Explanation:

Step1: Calculate side length from vertices

The distance between $(1, 7)$ and $(1, 4)$ is $|7-4| = 3$ units.

Step2: Find the other side length

Let the unknown side be $l$. Perimeter formula: $2(l+3)=10$
$\frac{2(l+3)}{2}=\frac{10}{2}$
$l+3=5$
$l=5-3=2$ units
Verify with area: $3\times2=6$ square units, which matches.

Step3: Find x-coordinate of missing vertices

Since the given side is vertical (same x=1), the missing vertices have x-coordinate $1+2=3$ or $1-2=-1$.

Step4: Identify full missing coordinates

The y-coordinates match the given vertices, so the pairs are $(3, 7)$ and $(3, 4)$, or $(-1, 7)$ and $(-1, 4)$.

Answer:

The two pairs of possible missing vertices are $\boldsymbol{(3, 7)}$ and $\boldsymbol{(3, 4)}$, or $\boldsymbol{(-1, 7)}$ and $\boldsymbol{(-1, 4)}$