### Home > GC > Chapter 10 > Lesson 10.1.4 > Problem10-42

10-42.

Quadrilateral $ABCD$ is graphed so that $A(3, 2)$, $B(1, 6)$, $C(5, 8)$, and $D(7, 4)$.

1. Graph $ABCD$ on graph paper. What shape is $ABCD$? Justify your answer.

Use the Pythagorean Theorem to find the lengths of the each side. What does it tell you about the shape?
Calculate the slope of each side. What does that tell you about each side that is next to each other?

2. $ABCD$ is rotated $180º$ about the origin to create $A'B'C'D'$. Then $A'B'C'D'$ is reflected across the $x$-axis to form $A''B''C''D''$. Name the coordinates of $C'$ and $D''$.

Use the eTool below to explore the graph of quadrilateral ABCD.
Click the link to the right for full version. GC 10-42 HW eTool  (Desmos)