Key Concepts
- Find vertical distance.
- Find horizontal distance.
- Solve problems using distance.
Introduction:
Finding the distance between two points on a coordinate plane:
When two points are in the same quadrant, we subtract to find the difference of their absolute values to find the distance between them.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3238.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3239.png)
When two points are in different quadrants, we add to find the difference of their absolute values to find the distance between them.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3240.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3241.png)
- If the x-coordinates are the same, we use the y-coordinates to find the distance.
- If the y-coordinates are the same, we use the x-coordinates to find the distance.
For example, if the coordinates are (3, 5) and (3, -2), use y-coordinates.
If the coordinates are (-1, 4) and (6, 4), use x-coordinates.
2.5.1 Find vertical distance
Example 1:
Find the distance between (-4, –1) and (-4, –6).
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-84.jpeg)
Solution:
Use absolute value. Look at the y-coordinates. Since the points are in the same quadrant, subtract the absolute values.
|-6| – |-1| = 6 – 1 = 5.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3242.png)
Example 2:
Find the distance from the Ferris wheel to roller coaster 3.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-85.jpeg)
Solution:
Find the coordinates of the Ferris wheel and the roller coaster 3.
- The coordinates of the Ferris wheel are (-6, 2).
- The coordinates of the roller coaster 3 are (-6, -8).
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-86.jpeg)
The absolute value of the y-coordinates tells you the distance between each point and the x-axis.
The distance from Ferris wheel to roller coaster 3 is
|2|+|-8| = 2 + 8 = 10 miles.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3243-1024x140.png)
2.5.2 Find horizontal distance
Example 3:
Find the distance between (-3, 5) and (4, 5).
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3244.png)
Solution:
Use absolute value. Look at the x-coordinates. Since the points are in the different quadrants, add the absolute values.
|-3| + |4| = 3 + 4 = 7.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3245.png)
Example 4:
Find the distance from roller coaster 1 to the swings.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3247.png)
Solution:
Find the coordinates of the roller coaster 1 and the swings.
- The coordinates of the roller coaster 1 are (-6, 7).
- The coordinates of the roller swings are (1, 7).
The distance from roller coaster 1 to the swings is
|-6|+|1| = 6 + 1 = 7 miles.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3246-1024x142.png)
2.5.3 Solve problems using distance
Example 5:
The graph shows the locations of point G and point H. Point J is graphed at (n, -3). The distance from point H to point J is equal to the distance from point H to point G.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3248.png)
- What is the distance from point H to point J?
- What is the value of n?
Solution:
Step 1:
Find the distance from point H to point J.
The x-coordinates are the same.
|-6|-|-3| = 6 – 3 = 3 units.
Step 2:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5296.png)
The distance from point H to point G is 3 units.
n – 0 =3
n = 3
Exercise:
- To find distances between points on a coordinate plane, we need to use _______________.
- We need to ___________ absolute values to find distance between two points using their coordinates if they lie in different quadrants.
- We need to _____________ absolute values to find distance between two points using their coordinates if they lie in the same quadrant.
- Find the distance between the points (5, —6) and (2, —6)
- Find the distance between each pair of points (-6, —4.7) and (-6, 4.1)
- Find the distance between the points (- 2 , 1 ) and (-1 , 1 )
- Find the distance between the points (-7, -4) and (-7, 9)
- Find the distance from the Roller Coaster 1 to Ferris Wheel.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5302.png)
9.Find the distance between the Water Park and the Coulter’s Home.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5305.png)
10. Find the distance between the school and the store.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5307.png)
Concept Map
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3252-1024x337.png)
What have we learned:
- Find vertical distance between two points on a coordinate plan.
- Find horizontal distance between two points on a coordinate plan.
- Solve problems using distance on a coordinate plan.
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