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Common Core Math8th GradeGeometry

8.G.8: Distance Between Two Points

Also written as 8.G.B.8 and CCSS.MATH.CONTENT.8.G.B.8 · Cluster: Understand and apply the Pythagorean Theorem.

Print 8.G.8 Graph PaperAll 28 8th Grade Math Standards

The Official Wording

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Common Core State Standards, Grade 8, Geometry · Read it at the source · Checked October 14, 2026

What 8.G.8 Means in Plain English

Eighth graders find the straight-line distance between two points by drawing a right triangle beneath it. From (1, 2) to (7, 10) the legs run 6 across and 8 up, so the distance is √(36 + 64) = √100 = 10 units.

No new formula is needed: the grid hands over the legs and the Pythagorean theorem does the rest, with negative coordinates counted carefully. High school turns the same move into the distance formula and uses it for perimeters and areas on the grid (HSG-GPE.7).

8.G.8 I Can Statements

  • I can draw a right triangle with a segment as its hypotenuse.
  • I can find leg lengths on a grid, even across an axis.
  • I can find the distance between two points with the Pythagorean theorem.

8.G.8 Worked Example

Two points on opposite sides of both axes, where counting across zero is the step students slip on.

Problem

Find the distance between A(−2, 5) and B(3, −7).

Distance from (−2, 5) to (3, −7)
  1. Plot both points and draw a right triangle with AB as its hypotenuse. Put the corner level with A and straight above B.right angle at C(3, 5)
  2. Horizontal leg: from x = −2 to x = 3. Crossing zero means 2 units to the axis plus 3 beyond it.AC = 3 − (−2) = 5
  3. Vertical leg: from y = 5 down to y = −7, across zero again.CB = 5 − (−7) = 12
  4. Use the Pythagorean theorem on the two legs.AB² = 5² + 12² = 25 + 144 = 169
  5. Take the square root.AB = √169 = 13 units
AnswerAB = 13 units.

Check it: The distance must be longer than either leg and shorter than the two legs walked end to end: 12 < 13 < 17. Marking the segment on a strip of paper and laying it along the grid gives about 13 too.

Common Mistakes with 8.G.8

Subtracting across zero wrongly

From x = −2 to x = 3 counted as 3 − 2 = 1

Try this: Count the grid squares for the first few problems, and match the count to 3 − (−2) = 5.

Adding the legs instead of their squares

AB = 5 + 12 = 17 units

Try this: Trace the two legs, then the slanted segment, with a finger. Cutting across is shorter than walking both legs, so it cannot be 17.

Squaring a negative difference wrongly

(−12)² written as −144, so AB² = 25 − 144

Try this: Write each leg as a length, which is never negative, before squaring. A negative number squared is positive anyway: (−12)² = 144.

Where 8.G.8 Fits

Comes Before6.NS.8Find distances between points that share a first or second coordinate.6.G.3Draw polygons on the coordinate plane and find the lengths of their sides.
Alongside8.G.7Use the theorem to find missing sides in real problems.8.EE.6Draw the same rise-and-run triangle that gives a line’s slope.
Comes Next
HSG-GPE.7Use the distance formula to find perimeters and areas on the coordinate plane.
HSG-GPE.4Use coordinates to prove simple geometric theorems.

Practice 8.G.8

Graph Paper GeneratorFree ToolFour-quadrant grids for plotting the two points and drawing the right triangle beneath the segment, with each leg labeled before any squaring.Four quadrantsCoordinate grid
Print Graph Paper

Quick Check

  1. Find the distance between (0, 0) and (9, 12).
  2. Find the distance between (−4, 1) and (2, 9).
  3. Find the distance between (1, 1) and (4, 3), to the nearest tenth.

8.G.8: Other Names

8.G.88.G.B.8CCSS.MATH.CONTENT.8.G.B.8

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.