Distance and Midpoint on a Coordinate Plane

Use coordinates to measure distance and locate the middle.

Lesson 3 of 42 parts Practice Flashcards

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Distance Formula

Objective: Compute the straight-line distance between two points.

For points (x₁,y₁) and (x₂,y₂), the horizontal and vertical differences form the legs of a right triangle. The Pythagorean theorem gives the distance.

Points A and B form the hypotenuse of a right triangle with horizontal change four and vertical change three.

Formulas

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Worked examples

Try itFind the distance from (0,0) to (3,4).Show answer

d = √(3² + 4²) = √25 = 5.

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Distance Formula

Objective: Compute the straight-line distance between two points.

For points (x₁,y₁) and (x₂,y₂), the horizontal and vertical differences form the legs of a right triangle. The Pythagorean theorem gives the distance.

Formulas

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Worked examples

Try itFind the distance from (0,0) to (3,4).Show answer

d = √(3² + 4²) = √25 = 5.

Midpoint Formula

Objective: Compute the midpoint of two coordinate points.

Average the x-coordinates and y-coordinates separately to find the midpoint.

A segment joins A and B on a coordinate plane. M is halfway along the segment.

Formulas

$M = ((x_1+x_2)/2,(y_1+y_2)/2)$

Worked examples

Try itFind the midpoint of (2,4) and (8,10).Show answer

M = ((2+8)/2,(4+10)/2) = (5,7).

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