FRACTIONAL DISTANCE FOR A NUMBER LINE FOR A

FRACTIONAL DISTANCE

FOR A NUMBER LINE…

FOR A COORDINATE PLANE…

EXAMPLE

Ex: Point P is located on the segment between point A(1, 4) and point D(7, 13). The distance from A to P is twice the distance from P to D. What are the coordinates of point P?

Determining the Distance between Two Points APPLYING THE DISTANCE FORMULA

What types of lines can we find distances between? WHY CAN WE ONLY FIND THE DISTANCE BETWEEN PARALLEL LINES?

Parallel Lines The shortest distance between two parallel lines is the length of the perpendicular ________ segment between them. doesn’t matter which perpendicular line you It ______ choose, as long as the two points are on the lines. How many perpendicular lines are in between two parallel lines? same Notice that all of the segments are the _____ length _______. So, when picking a perpendicular segment, be integers sure to pick one with endpoints that are _______.

Example 1 Find the distance between x=3 and x=− 5. What types of lines are these given the equations? -5 What formula do we use to solve this? ? 3

YOUR TURN: Find the distance between y=5 and y=− 6.

What is the shortest distance between y=2 x+4 and y=2 x− 1? 1. Determine the perpendicular slope to the lines. 2. Find a point on one of the lines. 3. Use the slope of the line perpendicular to ed lines to find the corresponding usthe e v a __, _ ld h point on the other line _ u _ o _ c you in_ts____ t o a _ p h _ t _ _ move m The down one unit and ce means __we e _ o _ *Notislope w a t _ s _ ***right __ _units. n the 2 _ o y _ n _ e a r _ a ___ they s a g lonthe corresponding line. point is…. . r as. So a l u c i d n e perp 4. Use the distance formula to find the length of the perpendicular segment, which is the distance between the lines. .

Example 3 Find the distance between the two parallel lines below. 1. Find the slope of the lines (if you find one, you find both). 2. Find the slope of the line perpendicular to the lines. 3. Find a point on one of the lines. 4. Use the slope of the line perpendicular to the lines to find the corresponding point on the other line Continue moving down 3 units, left one unit until you intersect the corresponding point on the other line. 5. . Use the distance formula to find the length of the perpendicular segment, which is the distance between the lines.

You try: Find the distance between the two parallel lines below.