Question

1. which best describes the relationship between line 1 and line 2?

line 1 passes through (2, - 7) and (4, - 3)
line 2 passes through (-4,9) and (-2,13)
a. perpendicular
b. parallel
c. same line
d. neither parallel nor perpendicular

1. if \\( \angle goh = 24 ^ { \circ } \\) and \\( \angle foh = 50 ^ { \circ } \\), what is the measure of \\( \angle fog \\)?

a. 31
b. 28
c. 23

Explanation:

Step1: Calculate the slope of Line 1

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
For Line 1 with \((x_1,y_1)=(2,-7)\) and \((x_2,y_2)=(4,-3)\), \(m_1=\frac{-3-(-7)}{4 - 2}=\frac{-3 + 7}{2}=\frac{4}{2}=2\).

Step2: Calculate the slope of Line 2

For Line 2 with \((x_1,y_1)=(-4,9)\) and \((x_2,y_2)=(-2,13)\), \(m_2=\frac{13 - 9}{-2-(-4)}=\frac{4}{-2 + 4}=\frac{4}{2}=2\).

Step3: Determine the relationship

Since \(m_1 = m_2=2\), the two lines are parallel.

Answer:

B. parallel