Problem preview

G-CO.5 Warmup M1-040-A01-V01

Draw transformed figures and specify transformation sequences mapping one figure to another.

Translate every vertex of a polygon by the same vector

Problem

Translate the polygon with vertices \(0,~0\); \(3,~0\); \(1,~2\) by the vector \(<4,-1>\).

Coordinate-plane source diagram presenting only the geometric information supplied in the prompt.

Big Picture

What this problem is really about

A polygon translation is one coordinate rule applied uniformly, not a separate decision at each vertex. Convert the vector into horizontal and vertical coordinate changes, apply both components to every vertex in the original order, and reconnect corresponding images so the side pattern and orientation remain intact.

Answer choices

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(4, 1); (7, 1); (5, 3)

(-4, 1); (-1, 1); (-3, 3)

(4, -1); (7, -1); (5, 1)

(1, 4); (4, 4); (2, 6)

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Curriculum context

Course: Math I
Standard: G-CO.5
Category: Geometry
Domain: Congruence
Objective: Draw transformed figures and specify transformation sequences mapping one figure to another.
Problem type: Translate every vertex of a polygon by the same vector