Question

determine whether $overleftrightarrow{km}$ and $overleftrightarrow{st}$ are parallel, perpendicular, or neither. k(-1, -8), m(1, 6), s(-2, -6), t(2, 10)
parallel
perpendicular
neither

Explanation:

Step1: Calculate slope of $\overleftrightarrow{KM}$

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $K(-1,-8)$ and $M(1,6)$, we have $m_{KM}=\frac{6 - (-8)}{1-(-1)}=\frac{6 + 8}{1 + 1}=\frac{14}{2}=7$.

Step2: Calculate slope of $\overleftrightarrow{ST}$

For points $S(-2,-6)$ and $T(2,10)$, using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m_{ST}=\frac{10-(-6)}{2 - (-2)}=\frac{10 + 6}{2+2}=\frac{16}{4}=4$.

Step3: Check relationship

Two lines are parallel if their slopes are equal ($m_1 = m_2$), and perpendicular if the product of their slopes is - 1 ($m_1\times m_2=-1$). Here, $m_{KM}=7$ and $m_{ST}=4$, $m_{KM}
eq m_{ST}$ and $m_{KM}\times m_{ST}=7\times4 = 28
eq - 1$.

Answer:

Neither