Solving Problems on the Coordinate Plane
Solving problems on the coordinate plane teaches Grade 5 students to use ordered pairs to represent real-world locations and find distances. To find the distance between two points on the same horizontal or vertical line, students subtract the differing coordinates: a library at (2,5) and a school at (2,9) are 9−5=4 blocks apart since they share x=2. A pirate ship at (4,3) and treasure at (6,3) are 6−4=2 paces apart since they share y=3. Students also calculate new positions by adding or subtracting from coordinates. This skill is from Pengi Math (Grade 5), Chapter 9.
Key Concepts
Property To find the distance between two points on the same horizontal or vertical line, find the difference of their non identical coordinates.
Examples On a city map, the library is at $(2, 5)$ and the school is at $(2, 9)$. Since they are on the same vertical line, the distance between them is $9 5 = 4$ blocks. A treasure map shows a pirate ship at $(4, 3)$ and a hidden treasure at $(6, 3)$. Since they are on the same horizontal line, the distance between them is $6 4 = 2$ paces. A zoo map marks the entrance at $(4, 4)$ and the lion exhibit is 2 units left and 1 unit down. Since left subtracts from the $x$ coordinate and down subtracts from the $y$ coordinate, the lion exhibit is at $(4 2, 4 1) = (2, 3)$.
Explanation The coordinate plane can be used to represent real world locations and solve problems involving distance. An ordered pair $(x, y)$ can describe the exact position of an object on a map or grid. To find the distance between two points that share a coordinate, you can simply count the units between them or subtract their coordinates that are different. This method works for finding lengths along straight horizontal or vertical paths.
Common Questions
How do you find the distance between two points on the coordinate plane?
If the points share an x-coordinate (same vertical line), subtract their y-coordinates. If they share a y-coordinate (same horizontal line), subtract their x-coordinates. The result is the distance.
A library is at (2,5) and a school is at (2,9). How far apart are they?
They share the same x-coordinate, so they are on a vertical line. Distance = 9 − 5 = 4 blocks.
A ship is at (4,3) and treasure is at (6,3). How far apart?
They share the same y-coordinate, so they are on a horizontal line. Distance = 6 − 4 = 2 paces.
How do you find a new position by moving left and down on a coordinate grid?
Subtract from the x-coordinate to move left, and subtract from the y-coordinate to move down. From (4,4), moving 2 left and 1 down gives (4−2, 4−1) = (2,3).
Can you only find distances for horizontal or vertical paths on the coordinate plane?
In Grade 5, yes. Finding distance between any two arbitrary points (diagonal paths) requires the Pythagorean theorem, which is taught in later grades.
What grade and chapter covers coordinate plane problem-solving?
Grade 5, Chapter 9: The Coordinate Plane in Pengi Math.