Lesson 11Finding Distances in the Coordinate Plane
Learning Goal
Let’s find distances in the coordinate plane.
Learning Targets
I can find the distance between two points in the coordinate plane.
I can find the length of a diagonal line segment in the coordinate plane.
Lesson Terms
- hypotenuse
- legs
- Pythagorean Theorem
Warm Up: Closest Distance
Problem 1
Order the following pairs of coordinates from closest to farthest apart. Be prepared to explain your reasoning.
and and and and and
Problem 2
Name another pair of coordinates that would be closer together than the first pair on your list.
Problem 3
Name another pair of coordinates that would be farther apart than the last pair on your list.
Activity 1: How Far Apart?
Problem 1
Find the distances between the three points shown.
Activity 2: Perimeters with Pythagoras
Problem 1
Which figure do you think has the longer perimeter?
Select one figure and calculate its perimeter. Your partner will calculate the perimeter of the other. Were you correct about which figure had the longer perimeter?
Are you ready for more?
Problem 1
Quadrilateral
Use the Pythagorean Theorem to find the lengths of sides
, , , and . Use the Pythagorean Theorem to find the lengths of the two diagonals,
and . Explain why quadrilateral
is a rectangle.
Activity 3: Finding the Right Distance
Problem 1
Have each person in your group select one of the sets of coordinate pairs shown here. Then calculate the length of the line segment between those two coordinates. Once the values are calculated, have each person in the group briefly share how they did their calculations.
-
and -
and -
and -
and
How does the value you found compare to the rest of your group?
In your own words, write an explanation to another student for how to find the distance between any two coordinate pairs.
Lesson Summary
We can use the Pythagorean Theorem to find the distance between any two points on the coordinate plane. For example, if the coordinates of point
Think of the distance between
The length of the horizontal leg is 6, which can be seen in the diagram, but it is also the distance between the
Once the lengths of the legs are known, we use the Pythagorean Theorem to find the length of the hypotenuse,
This length is a little longer than 9, since 85 is a little longer than 81. Using a calculator gives a more precise answer,