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Algebra Difficulty 1.6 Junior Find the answer Canada

The operation $\Delta$ is defined so that $a \Delta b = a \times b + a + b$ . For example, $2 \Delta 5 = 2\times 5+2+5=17$ . If $p \Delta 3 = 39$ , the value of $p$ is

Pick one

Solution

To find the image of $PQ$ , we reflect points $P$ and $Q$ across the $x$ -axis, then join them.

Since $P$ is 3 units above the $x$ -axis, then the reflection of $P$ across the $x$ -axis is 3 units below the $x$ -axis at the same $x$ -coordinate.

That is, point $T$ is the image of $P$ after it is reflected across the $x$ -axis.

Similarly, after a reflection across the $x$ -axis, the image of point $Q$ will be 6 units below the $x$ -axis but have the same $x$ -coordinate as $Q$ .

That is, point $U$ is the image of $Q$ after it is reflected across the $x$ -axis.
Therefore, the line segment $TU$ is the image of $PQ$ after it is reflected across the $x$ -axis.

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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.