Problem preview

G-GPE.1 Warmup M2-041-A12-V04

Derive the equation of a circle from center/radius and complete the square to identify center/radius.

Interpret a contextual circle boundary and covered region

Problem

A drone signal map uses coordinates in kilometers and has boundary equation \((x~-~7)^{2}~+~(y~+~2)^{2}~=~49\). Identify the drone location and range, explain what equality represents, and write the inequality for the entire signal-covered region.

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The drone is at (7,−2) and its signal reaches only points exactly 7 km away.

The drone is at (7,−2) and its signal covers all points within 7 km, so (x−7)²+(y+2)² ≤ 49.

The drone is at (7,−2) and its signal covers all points within 49 km.

The drone is at (−7,2) and its signal covers all points within 7 km.

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Curriculum context

Course: Math II
Standard: G-GPE.1
Category: Geometry
Domain: Expressing Geometric Properties with Equations
Objective: Derive the equation of a circle from center/radius and complete the square to identify center/radius.
Problem type: Interpret a contextual circle boundary and covered region