Four friends are touring on motorcycles. They come to an intersection of two roads ;the road they are on continues straight, and the other is perpendicular to it. The sign at the intersection shows the distances to several towns. Draw a map/diagram of the roads and use it and the information on the sign to answer the following questions:
What is the distance between Albertsville and Dewey Falls?
What is the distance between Blossville and Cheyenne?
On the coordinate plane, what represents the intersection of the two roads?
Example 1: The Distance Between Points on an Axis
What is the distance between (-4, 0) and (5, 0)?
What do the ordered pairs have in common and what does that mean about their location in the coordinate plane?
How did we find the distance between two numbers on the number line?
Use the same method to find the distance between (-4, 0) and (5, 0).
Example 2: The Length of a Line Segment on an Axis
What is the length of the line segment with endpoints (0, -6) and (0, 11)?
What do the ordered pairs of the endpoints have in common and what does that mean about the line segment’s location in the coordinate plane?
Find the length of the line segment described by finding the distance between its endpoints (0, -6) and (0, 11)?
Find the length of the line segment by finding the distance between its endpoints (-3, 3) and (-3, -5)
1. Find the lengths of the line segments whose endpoints are given below. Explain how you determined that the line segments are horizontal or vertical.
a) (-3, 4), (-3, 9)
b) (2, -2), (-8, -2)
c) (-6, -6), (-6, 1)
d) (-9, 3), (-4, 4)
e) (0,-11), (0, 8)
To find the distance between points that lie on the same horizontal line or on the same vertical line, we can use the same strategy that we used to find the distance between points on the number line.
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