Problem preview

G-GPE.4 Warmup M1-044-A08-V03

Use coordinates, distance, and algebra to prove or disprove simple geometric statements.

Use coordinates to prove or disprove a right triangle

Problem

Use coordinates to decide whether points \(L(1,~1)\), \(M(4,~5)\), and \(N(8,~2)\) form a right triangle.

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Right triangle; the slopes of LM and MN are 4/3 and -3/4, and one positive slope and one negative slope means the sides are perpendicular.

Not a right triangle; the slopes of LM and MN are 4/3 and -3/4, and since they are not equal, the sides are not perpendicular.

Not a right triangle; the slopes of LM and MN are 4/3 and -3/4, and because they are different fractions, they cannot form a right angle.

Right triangle; the slopes of LM and MN are 4/3 and -3/4, which are negative reciprocals, so those sides are perpendicular.

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Curriculum context

Course: Math I
Standard: G-GPE.4
Category: Geometry
Domain: Expressing Geometric Properties with Equations
Objective: Use coordinates, distance, and algebra to prove or disprove simple geometric statements.
Problem type: Use coordinates to prove or disprove a right triangle