Question

1. determine whether line st and line lm are parallel, perpendicular, or neither. s(6, -1) t(8, 3) l(0, 10) m(-2, 9) a. parallel b. perpendicular c. neither 10. what is the length, to the nearest tenth, of the line segment joining the points (-4, 2) and (146, 52)? a. 141.4

Explanation:

Step1: Calculate the slope of line ST

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $S(6,-1)$ and $T(8,3)$, we have $m_{ST}=\frac{3-(-1)}{8 - 6}=\frac{4}{2}=2$.

Step2: Calculate the slope of line LM

For points $L(0,10)$ and $M(-2,9)$, we have $m_{LM}=\frac{9 - 10}{-2-0}=\frac{-1}{-2}=\frac{1}{2}$.

Step3: Analyze the relationship between the slopes

Two lines are parallel if their slopes are equal. Since $m_{ST}=2$ and $m_{LM}=\frac{1}{2}$, they are not equal. Two lines are perpendicular if the product of their slopes is - 1. Since $m_{ST}\times m_{LM}=2\times\frac{1}{2}=1
eq - 1$, the lines are neither parallel nor perpendicular.

Step4: Calculate the length of the line - segment

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $(-4,2)$ and $(146,52)$, we have:
\[

$$\begin{align*} d&=\sqrt{(146-(-4))^2+(52 - 2)^2}\\ &=\sqrt{(150)^2+(50)^2}\\ &=\sqrt{22500 + 2500}\\ &=\sqrt{25000}\\ &=50\sqrt{10}\approx158.1 \end{align*}$$

\]

Answer:

1. C. Neither
2. a. 158.1