Question

1. determine if given two points if the lines are parallel, perpendicular or neither.

line 1 (-2, 5), (-2, 7) and line 2 (5,1), (5,13)

Explanation:

Step1: Find slope of Line 1

For points \((x_1,y_1)=(-2,5)\) and \((x_2,y_2)=(-2,7)\), slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_2 - x_1=-2 - (-2)=0\), so slope \(m_1\) is undefined (vertical line).

Step2: Find slope of Line 2

For points \((x_1,y_1)=(5,1)\) and \((x_2,y_2)=(5,13)\), \(x_2 - x_1=5 - 5 = 0\), so slope \(m_2\) is undefined (vertical line).

Step3: Compare slopes

Two vertical lines are parallel. So Line 1 and Line 2 are parallel.

Answer:

The lines are parallel.