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Type: Multiple-Choice
Category: Points, Lines, and Planes
Level: Grade 10
Standards: HSG-CO.C.9
Author: nsharp1
Created: 6 years ago

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Points, Lines, and Planes Question

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In the diagram given, lines

$k$ and

$m$ are parallel, and line

$t$ is a transversal. Let point

$A$ be the intersection of lines

$k$ and

$t$ , and point

$B$ be the intersection of lines

$m$ and

$t$ (points not labeled in the diagram). Also, let

$h$ be the line parallel to lines

$k$ and

$m$ which is equidistant from these two lines (not pictured).

Grade 10 Points, Lines, and Planes CCSS: HSG-CO.C.9

Which of the following reasons ensures that lines

$k$ and

$m$ are coincident after the translation by

$vec{AB}$ , given that line

$k$ now passes through point

$B?$

Rigid transformations don't change size or shape.
No rotations or reflections were used in the transformation, thus the slope of the line cannot change.
Point $A$ maps to point $B$ , and point $A$ was on line $k$ , thus these two points define a line, which is $k$ .
The Parallel Postulate and the fact that the slope of line $k$ remains unchanged by translations.