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.

   Hint (a):

   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 $\overleftrightarrow{BD}$.

   Hint (b):

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

   Partial Answer:

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

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

   Hint (c):

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