What is the reflection of $(-2,3)$ in the line $y = -x$?
A. $(3,-2)$
B. $(3,2)$
C. $(-3,2)$
D. $(-3,-2)$
Answer (2)
The reflection of the point ( − 2 , 3 ) in the line y = − x is ( − 3 , 2 ) . Therefore, the correct answer is option C: ( − 3 , 2 ) .
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To reflect a point across the line y = − x , we swap the x and y coordinates and negate them.
Given the point ( − 2 , 3 ) , we apply the reflection rule.
The x -coordinate becomes − 3 , and the y -coordinate becomes − ( − 2 ) = 2 .
The reflected point is ( − 3 , 2 ) .
Explanation
Understanding the Reflection Rule To find the reflection of a point across the line y = − x , we swap the x and y coordinates and negate them. In other words, the reflection of the point ( x , y ) is the point ( − y , − x ) .
Applying the Rule to the Given Point We are given the point ( − 2 , 3 ) . Applying the reflection rule, we swap the coordinates and negate them. So, the x -coordinate becomes − 3 , and the y -coordinate becomes − ( − 2 ) = 2 . Therefore, the reflected point is ( − 3 , 2 ) .
Final Answer The reflection of the point ( − 2 , 3 ) in the line y = − x is ( − 3 , 2 ) .
Examples
Reflecting points across lines is useful in computer graphics for creating symmetrical images or animations. For example, if you are designing a logo and want it to be symmetrical about a diagonal axis, you can reflect certain elements across the line y = − x to achieve the desired symmetry. This technique is also used in physics to analyze the behavior of particles when they collide with a surface.
