Question

3.5 identifying and writing parallel and perpendicular lines
in exercises 1 - 2, determine which lines are parallel and which of these lines are perpendicular.
1.
2.
in exercises 3 - 6, tell whether the lines through the given points are parallel, perpendicular, or neither.

1. line 1: (1,0),(7,4)

line 2: (7,0),(3,6)

1. line 1: (-3,1),(-7,-2)

line 2: (2,-1),(8,4)

1. line 1: (-9,3),(-5,7)

line 2: (-11,6),(-7,2)

1. line 1: (10,5),(-8,9)

line 2: (2,-4),(11,-6)

Explanation:

Step1: Calculate the slope of a line

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
For line 1 with points \((1,0)\) and \((7,4)\):
\(m_1=\frac{4 - 0}{7 - 1}=\frac{4}{6}=\frac{2}{3}\)
For line 2 with points \((7,0)\) and \((3,6)\):
\(m_2=\frac{6 - 0}{3 - 7}=\frac{6}{-4}=-\frac{3}{2}\)

Step2: Determine the relationship

Two lines are parallel if \(m_1 = m_2\), and perpendicular if \(m_1\times m_2=- 1\).
Here, \(m_1\times m_2=\frac{2}{3}\times(-\frac{3}{2})=-1\)

Answer:

The lines are perpendicular.