Question

the graph shows two vertices of a rectangle. the rectangle has a width of 6 units and a length of 8 units. plot the other two vertices.

Explanation:

Step1: Identify coordinates of given points

Point $A$: $(-2, 2)$, Point $B$: $(4, 4)$

Step2: Calculate horizontal/vertical differences

Horizontal distance between $A$ and $B$: $|4 - (-2)| = 6$, Vertical distance: $|4 - 2| = 2$
Since width=6, length=8, we use the horizontal difference as width, then find length along vertical.

Step3: Find first missing vertex

From $A$, add 8 units vertically down: $(-2, 2 - 8) = (-2, -6)$

Step4: Find second missing vertex

From $B$, add 8 units vertically down: $(4, 4 - 8) = (4, -4)$
Alternative: We can also add 8 units up, giving $(-2, 10)$ and $(4, 12)$, but the downward pair fits the grid better.

Answer:

The two missing vertices are $\boldsymbol{(-2, -6)}$ and $\boldsymbol{(4, -4)}$ (or $\boldsymbol{(-2, 10)}$ and $\boldsymbol{(4, 12)}$ as a valid upper-plane alternative). When plotted, these form a rectangle with the given points, satisfying width=6 and length=8.