### Home > INT1 > Chapter 8 > Lesson 8.1.3 > Problem8-42

8-42.

Graph the quadrilateral $ABCD$ if $A(−2, 6)$, $B(2, 3)$, $C(2, −2)$, and $D(−2, 1)$.

1. A rhombus is a quadrilateral with four congruent sides. Verify that $ABCD$ is a rhombus.

Use the Pythagorean Theorem, to find the distance of each side. Verify that all sides have the same length.

2. What is the area and perimeter of $ABCD$?

Can you find the length of the base? Can you find the height of the rhombus?

3. What is the slope of the diagonals, $\overline{AC}$ and $\overline{BD}$? How are these diagonals related?

Read the Math Notes box in Lesson 3.3.6 on parallel and perpendicular lines.

4. What is the point of intersection of the diagonals? What is the relationship between this point and diagonal $\overline{AC}$?

Use the eTool below to answer the following questions.
Click the link at right for the full version of the eTool: Int1 8-42 HW eTool