Problem preview

G-GPE.4 Warmup M2-043-A10-V04

Use coordinates to prove simple geometric theorems, including simple circle theorems.

Disprove a claim with a specified coordinate calculation

Problem

Disprove the claim that triangle \(ABC\) is right at \(B\). Calculate or use the supplied slopes \(\text{mAB}~=~1/2\) and \(\text{mBC}~=~2/3\), test the perpendicularity condition by their product, and state the corrected angle conclusion.

Answer choices

Choose your path.

Preview only

mAB = 1/2 and mBC = 3/2; their product is 3/4, so ∠ABC is not right.

Both slopes are positive, so ∠ABC is right.

mAB = 1/2 and mBC = 2/3; their product is 1/3, not −1, so ∠ABC is not right.

The slope product 1/3 is positive, so ∠ABC is right.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Inside Gozunta

More than a preview

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now

Curriculum context

Course: Math II
Standard: G-GPE.4
Category: Geometry
Domain: Expressing Geometric Properties with Equations
Objective: Use coordinates to prove simple geometric theorems, including simple circle theorems.
Problem type: Disprove a claim with a specified coordinate calculation