Lesson 14Distances on a Coordinate Plane
Learning Goal
Let’s explore distance on the coordinate plane.
Learning Targets
I can find horizontal and vertical distances between points on the coordinate plane.
Lesson Terms
- quadrant
Warm Up: Coordinate Patterns
Problem 1
Plot points in your assigned quadrant and label them with their coordinates.
Print Version
Plot points in your assigned quadrant and label them with their coordinates.
Activity 1: Signs of Numbers in Coordinates
Problem 1
Next to each point, write its coordinates with the Text tool or Pen tool.
Print Version
Write the coordinates of each point.
Problem 2
Answer these questions for each pair of points.
How are the coordinates the same? How are they different?
How far away are they from the y-axis? To the left or to the right of it?
How far away are they from the x-axis? Above or below it?
and and and
Pause here for a class discussion.
Problem 3
Point
Plot point
on the coordinate plane and label it with its coordinates. How far away are
and from the -axis? What is the distance between
and ?
Print Version
Point
Plot point
on the coordinate plane and label it with its coordinates. How far away are
and from the -axis? What is the distance between
and ?
Problem 4
Point
Plot point
on the coordinate plane and label it with its coordinates. How far away are
and from the -axis? What is the distance between
and ?
Print Version
Point
Plot point
on the coordinate plane and label it with its coordinates. How far away are
and from the -axis? What is the distance between
and ?
Problem 5
Point
Activity 2: Finding Distances on a Coordinate Plane
Problem 1
Label each point with its coordinates.
Print Version
Label each point with its coordinates.
Problem 2
Find the distance between each of the following pairs of points.
Point
and Point
and Point
and
Problem 3
Which of the points are 5 units from
Problem 4
Which of the points are 2 units from
Problem 5
Plot a point that is both 2.5 units from
Are you ready for more?
Problem 1
Priya says, “There are exactly four points that are 3 units away from
Do you agree with either of them? Explain your reasoning.
Lesson Summary
The points
Notice that the vertical distance between points
We can always tell which quadrant a point is located in by the signs of its coordinates.
quadrant | ||
---|---|---|
positive | positive | I |
negative | positive | II |
negative | negative | III |
positive | negative | IV |
In general:
If two points have
-coordinates that are opposites (like 5 and -5), they are the same distance away from the vertical axis, but one is to the left and the other to the right. If two points have
-coordinates that are opposites (like 2 and -2), they are the same distance away from the horizontal axis, but one is above and the other below.
When two points have the same value for the first or second coordinate, we can find the distance between them by subtracting the coordinates that are different. For example, consider
They have the same