Question

e, f, and h are three of the vertices of rectangle efgh on the coordinate plane. what are the coordinates of g, the fourth vertex of the rectangle?

Explanation:

Step1: Identify coordinates of known vertices

Let the coordinates of $E=(6,4)$, $F=(6, - 5)$, $H=(-7,4)$.

Step2: Use property of rectangle

In a rectangle, opposite sides are parallel. The $x$-coordinate of $G$ will be the same as the $x$-coordinate of $H$ and the $y$-coordinate of $G$ will be the same as the $y$-coordinate of $F$.

Step3: Determine coordinates of $G$

The $x$-coordinate of $G$ is $-7$ and the $y$-coordinate of $G$ is $-5$. So the coordinates of $G$ are $(-7,-5)$.

Answer:

$(-7,-5)$