Question

vt is the diagonal of a rhombus.
what is the slope of the other diagonal?
a. $\frac{2}{5}$
b. $\frac{5}{2}$
c. $-\frac{2}{5}$
d. $-\frac{5}{2}$

Explanation:

Step1: Find the slope of diagonal VT

The coordinates of $V(3,2)$ and $T(5,7)$. The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. So the slope of $VT$ is $m_{VT}=\frac{7 - 2}{5 - 3}=\frac{5}{2}$.

Step2: Use the property of diagonals of a rhombus

The diagonals of a rhombus are perpendicular to each other. If the slopes of two perpendicular lines are $m_1$ and $m_2$, then $m_1\times m_2=- 1$. Let the slope of the other diagonal be $m$. We know $m_{VT}=\frac{5}{2}$, so $\frac{5}{2}\times m=-1$. Solving for $m$, we get $m =-\frac{2}{5}$.

Answer:

C. $-\frac{2}{5}$