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Find Distances on the Coordinate Plane

Students graph points with rational coordinates in all four quadrants and use absolute value to find the distance between two points that share the same x-coordinate or the same y-coordinate. They apply this skill to find perimeters of polygons drawn on the coordinate plane.

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Find Distances on the Coordinate Plane

Grade 6 · Negative Numbers and the Number Line · question 1 of 3

0 of 20

20 rungs. A star at the top.

(3, −4) and (3, 0): distance =

How it is taught

0:00 of 3:27

On a horizontal segment, the y-coordinates match.

Distance is the positive difference of the x-coordinates.

Read it: Distance along a gridline

P(−4, 2) and Q(3, 2) share their second number, so they sit on one gridline. The y-axis lies between them at M. P is 4 from M and Q is 3 from it, so the distance is 4 + 3 = 7.

  1. Find the number the two points share: they sit on that gridline.
  2. On opposite sides of an axis, add their two distances to it.
  3. On one side of it, take the smaller distance from the larger.

The axis is where the line crosses 0, so each point's distance to it is its number without the sign.

Across the axis the two pieces lie end to end, so they add: 4 + 3 = 7.

On one side the nearer point sits inside the farther one's distance, so the difference is what is left.

Same side of the axis: subtract the distances. Opposite sides: add them.

Taking 3 from 4 across the axis, and getting 4 − 3 = 1.

P and Q are on opposite sides of the y-axis, so the distances add: 4 + 3 = 7.

(11, −6) and (11, 2): distance = ___ — 8. They share the first number, and they are on opposite sides of the x-axis: 6 + 2 = 8.

Distance from A(−3, 4) to B(2, 4)

Today we'll find the distance between two points on the coordinate plane.

Here's our coordinate plane, with the x-axis and y-axis crossing at zero.

Plot point A at negative three, four — three left of zero, four up.

Plot point B at two, four — two right of zero, four up.

Both points share the same y-coordinate, so they sit on the same horizontal line.

The distance from A to B is just the length of this segment between them.

Since A is left of zero and B is right of zero, we add their distances from zero — their absolute values.

The absolute value of negative three is three — that's how far A is from zero.

The absolute value of two is two — that's how far B is from zero.

How far is A(−3, 4) from B(2, 4)?Two points, same height — find the distance.Find the distance from A to B0xy−342A(−3, 4)B(2, 4)32|−3| = 3|2| = 23 + 2 = 5distance from A to BDISTANCE5units
Grade 6 · Using absolute value to find horizontal distance

Now add them together: three plus two equals five.

The distance from A to B is five units. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
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Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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