MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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9.3 Three-Dimensional Coordinate Geometry

Focus on distance in space and sphere equation.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Points and distance in spaceWorked steps · five questions02Equations of spheresWorked steps · five questions
Lesson brief and rules

9.3 Three-Dimensional Coordinate Geometry

Distance in space is (Δx)2+(Δy)2+(Δz)2\sqrt{(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}}.

Worked example 11
01 / Find the distance between (0,0,0)(0,0,0) and (12,16,0)(12,16,0).
02 / (12)2+(16)2+02=20\sqrt{(12)^{2}+(16)^{2}+0^{2}}=20.
03 / Answer: 2020
Worked example 2 · Sphere equation

A sphere centered at origin has radius 44. Choose its equation.

Squared distance from the origin equals r2r^{2}. Answer: x2+y2+z2=16x^{2}+y^{2}+z^{2}=16

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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