3.6 Perpendiculars and Distance

Key Concept

1. The distance from a line to a point not on the line is the length of the segment perpendicular to the line from the point.

2. The distance between two parallel lines is the distance between one of the lines and any point on the other line.

Theorem

• Theorem 3.9 – In a plane, if two lines are equidistant from a third line, then the two lines are parallel to each other.

Construction – Perpendicular Segment

Turn to Pg 160 – example 2.

Examples1. Find the distance from line s y = -x and V(1,

5)

2. Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and y = 2x – 3 respectively.

Homework

• Pg 163 # 19 – 27, 34, 35– On 25 – 27 only find the distance between the

point and the line.