Lesson 6: Determine Distance on the Coordinate Plane6.NOS.9

I can…

I can find the distance between two points on the coordinate plane using absolute value.

Key words

• Distance on the Coordinate Plane — The nonnegative distance between points, found from the absolute difference of coordinates on a horizontal or vertical line.
• Distance — How far apart two points are. It is never negative.
• Absolute value — How far a number is from zero. It is never negative.
• Horizontal distance — How far apart two points are going left or right.
• Vertical distance — How far apart two points are going up or down.
• Coordinate plane — A grid with a line going across and a line going up to plot points.
• Integer — Whole numbers and their opposites, like -2, -1, 0, 1, 2.
• Quadrant — One of the four regions of the coordinate plane, numbered I to IV.

Steps

1. I will find the distance from (-3, 2) to (4, 2). Both have y = 2, so they sit on the same horizontal line.
2. The points are on opposite sides of zero, so I add the absolute values.
3. |-3| = 3 and |4| = 4.
4. I add: 3 + 4 = 7. The distance between them is 7 units.

Try it

What is the distance between the points (2, -6) and (2, 3)?

Check your answer

9 units

Both points share x = 2, so this is a vertical distance. |3 - (-6)| = |3 + 6| = 9 units.

Sentence starter

I know ___ because ___.

Goal: I can explain my work using the words distance, absolute value, horizontal distance, and vertical distance.