Question

1. use the given figure. (6 points)

a. name a segment skew to vw
b. name a pair of parallel planes. plane and plane
c. name a segment parallel to yz

1. use the given figure. (6 points)

a. which transversal makes ∠12 and ∠14 alternate interior angles?
b. if line d is the transversal for lines a and b, name a pair of corresponding angles. and

1. use the given figure. p || q (8 points)

a. name a pair of consecutive interior angles. and
b. name a pair of alternate exterior angles. and

1. find the slope of the line through (7,4) and (5,9). then find the slope of the line parallel to it and the slope of the line perpendicular to it. (8 points)

m=
m||=
m⊥=

Explanation:

Step1: Slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given two points \((x_1,y_1)=(7,4)\) and \((x_2,y_2)=(5,9)\).

$$m=\frac{9 - 4}{5 - 7}=\frac{5}{-2}=-\frac{5}{2}$$

Step2: Slope of parallel line

Parallel lines have the same slope. So \(m_{\parallel}=-\frac{5}{2}\)

Step3: Slope of perpendicular line

The slope of a line perpendicular to a line with slope \(m\) is \(m_{\perp}=-\frac{1}{m}\). Substituting \(m =-\frac{5}{2}\), we get \(m_{\perp}=\frac{2}{5}\)

Answer:

\(m =-\frac{5}{2}\)
\(m_{\parallel}=-\frac{5}{2}\)
\(m_{\perp}=\frac{2}{5}\)