Curriculum placement
Grade 8. This describes the skill, not a learner estimate.
Distance in the coordinate plane
Find distance between two coordinate points
Problem types
- Distance between two points
- Exact distance between two points
- Midpoints, endpoints and circle centers
Builds on
- The Pythagorean theorem
- Coordinates in four quadrants
- Side lengths from coordinates · Earlier idea
Horizontal and vertical side lengths are found by counting units, and slanted sides use the Pythagorean theorem.
- Equations with one square root · Useful idea
The distance formula contains a square root, so finding a point at a given distance solves a square root equation.
Leads to
- What slides, flips, and turns keep the same
- Equations of circles
- Perimeter and area from coordinates
- Proofs that use coordinates
- A parabola as points equally far from a focus and a line
- Polar and Cartesian coordinates
- Vectors and their components
- Side ratios of special right triangles · See it applied
The distance from (0, 0) to (1, 1) is the square root of 2, which is the hypotenuse of a 45-45-90 triangle.
Related skills
- A graph as the solution set · Shared foundations
- Sine, cosine, and tangent · Shared foundations
- Translations, reflections, and rotations · Shared foundations
- Scatter plots and trend lines · Shared foundations
- Dividing a segment in a given ratio · Shared foundations
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