2015 CEMC Gauss (Grade 8) Problems/Problem 13

Problem

In the graph shown, which of the following represents the image of the line segment $PQ$ after a reflection across the $x$ -axis?

An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.

$\textbf{(A)}\ PS \qquad\textbf{(B)}\ TU \qquad\textbf{(C)}\ MN \qquad\textbf{(D)}\ WV \qquad\textbf{(E)}\ FG$

Solution 1

For the line segment to have been reflected across the $x$ -axis, each point on $PQ$ would have had the same $x$ coordinate, while having a negated $y$ coordinate.

Let $P'$ be the point $P$ after being reflected across the x-axis. We can see that point $P$ is at $(3, 3)$ . Thus, $P'$ must be located at $(3, -3)$ .

Using the graph, we see that $\boxed {\textbf {(B) } TU}$ is the only line segment that has that point.

We could have also used other points on the line segment to get the same result (ex. $Q$ )

~anabel.disher

Solution 2

We can use the fact that the slope would be negative due to the slope of the original line segment being positive and the line being flipped over the $x$ axis. This eliminates $FG$ and $WV$ because they both have positive slopes.

We can now use the fact that the $y$ coordinate would be negative because flipping over the $x$ -axis would result in a negative $y$ coordinate if the original line segment has a positive $y$ coordinate. Of the answer choices remaining, $\boxed {\textbf {(B) } TU}$ is the only one that fits the description.

~anabel.disher

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2015 CEMC Gauss (Grade 8) Problems/Problem 13

Problem

Solution 1

Solution 2