Home > CCG > Chapter Ch7 > Lesson 7.3.2 > Problem7-131

7-131.

Tomika remembers that the diagonals of a rhombus are perpendicular to each other.

1. Graph $ABCD$ if $A(1,4)$, $B(6,6)$, $C(4,1)$, and $D(−1,−1)$. Is $ABCD$ a rhombus? Show how you know.

Compare the lengths of all four sides.

2. Find the equations of the lines on which the diagonals lie. That is, find the equations of $\overleftrightarrow{AC}$ and $\overleftrightarrow{BD}$.

Find the slopes and the $y$-intercepts of the lines and write the equations of the lines in slope-intercept form ($y=mx+b$).

Equation for line $AC$: $y=-x+5$

3. Compare the slopes of $\overleftrightarrow{AC}$ and $\overleftrightarrow{BD}$. What do you notice?

What do you know about the slopes of parallel and perpendicular lines?

Use the eTool below to visualize the problem and answer all the parts.
Click the link at right for the full version of the eTool: 7-131 HW eTool (Desmos)