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CEMC Gauss (Grade 8), 2013

Geometry Difficulty 1.3 Junior Find the answer Canada

The point $(-2,-3)$ is reflected in the $x$ -axis.

What are the coordinates of its image after the reflection?

Pick one

Solution

When $n=4$ , we are looking for an expression that produces a value of 7.
The results of substituting $n=4$ into each expression and evaluating are shown below.

Expression	Value
(A) $3n-2$	$3(4)-2=12-2=10$
(B) $2(n-1)$	$2(4-1)=2(3)=6$
(C) $n+4$	$4+4=8$
(D) $2n$	$2(4)=8$
(E) $2n-1$	$2(4)-1=8-1=7$

Since $2n-1$ is the only expression which gives a value of 7 when $n=4$ , it is the only possible answer. We check that the expression $2n-1$ does give the remaining values, $1,3,5,9$ , when $n=1,2,3,5$ , respectively.
(Alternately, we may have began by substituting $n=1$ and noticing that this eliminates answers (B), (C) and (D). Substituting $n=2$ eliminates (A). Substituting $n=3$ , $n=4$ and $n=5$ confirms the answer (E).)

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.