Parallel lines$-$identical slope so they never intersect each other, unless overlapped.

Perpendicular lines$-$two lines form right angles to each other when they intersect. If the slope of first line is

${a \over b}$, the slope of perpendicular line is the slope of perpendicular line is

$- {b \over a}$. The product of the two slopes is -1.

Introduction

a)

- Definition of Parallel and Perpendicular Lines
- How does that relate to slope?

1.

Determine whether the three points A (-2,-1), B(0,4) & C(2,9) all lie on the same line.

2.

Determine the following slopes are parallel, perpendicular, or neither.

i) $m_1 = {2 \over 5}, m_2= {2 \over 5}$

ii) $m_1 = {1 \over5} , m_2 = - {5 \over 1}$

iii) $m_1 = {4 \over 7}, m_2 = {12 \over 21}$

iv) $m_1 =$undefined, $m_2 = 0$

v) $m_1 =mn^{-1}; m_2 =-m^{-1}b$

3.

Given the points of two lines, determine when the lines are parallel, perpendicular or neither.

a)

Line 1: (3,2) & (1,4); Line 2: (-1,-2) & (-3,-4)

b)

Line 1: (5,6) & (7,8); Line 2: (-5,-6) & (-7,-8)

c)

Line 1: (0,4) & (-1,2); Line 2: (-3,5) & (1,7)

4.

Show that the points A(-3,0), B(1,2) and C(3,-2) are the vertices of a right triangle.

5.

Show that the points A(-1,-1), B(3,0), C(2,4) and D(-2,3) are the vertices of a square.