QuestionFind the pre-image of vertex $A^{\prime}(8,5)$ after reflection across the $y$ -axis. Options: $(-8,-6)$ , $(-6,8)$ , $(8,6)$ , $(6,-8)$ .

Studdy Solution

STEP 1

Assumptions1. The image was created by a reflection across the y-axis. . The coordinates of the image vertex $A^{\prime}$ are $(8,5)$ .
3. The pre-image of vertex $A^{\prime}$ is one of the following options $(-8,-6)$ , $(-6,8)$ , $(8,6)$ , $(6,-8)$ .

STEP 2

A reflection across the y-axis changes the sign of the x-coordinate while the y-coordinate remains the same. Therefore, the pre-image of a point $(x,y)$ after reflection across the y-axis is $(-x,y)$ .

STEP 3

Apply this rule to the coordinates of vertex $A^{\prime}$ to find the coordinates of the pre-image.
$Pre-image = (-x,y)$

STEP 4

Substitute the given coordinates of $A^{\prime}$ into the formula.
$Pre-image = (-(8),)$

STEP 5

Calculate the x-coordinate of the pre-image.
$Pre-image = (-8,5)$ The pre-image of vertex $A^{\prime}$ is $(-8,5)$ . However, this option is not listed among the given options. Therefore, there seems to be a mistake in the problem or the given options. The correct pre-image should be $(-8,5)$ based on the rules of reflection across the y-axis.

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