Question

answer the question below. type your response in the space provided. 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: Find coordinates of E, F, H

From the graph: \( E(6, 4) \), \( F(6, -5) \), \( H(-6, 4) \).

Step2: Determine properties of rectangle

In a rectangle, opposite sides are equal and parallel. So, \( \overrightarrow{EH} \) and \( \overrightarrow{FG} \) should be equal, \( \overrightarrow{EF} \) and \( \overrightarrow{HG} \) should be equal.
The vector from \( E \) to \( H \) is \( (-6 - 6, 4 - 4)=(-12, 0) \). The vector from \( F \) to \( G \) should be the same. So, \( G = F + (-12, 0)=(6 - 12, -5 + 0)=(-6, -5) \).
Or, the vector from \( E \) to \( F \) is \( (6 - 6, -5 - 4)=(0, -9) \). The vector from \( H \) to \( G \) should be the same. So, \( G = H + (0, -9)=(-6, 4 - 9)=(-6, -5) \).

Answer:

\((-6, -5)\)