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A point P is reflected in the x - axis ....

A point P is reflected in the x - axis . Co - ordinates of its image are (8,-6).
Find the co - ordinates of the image of P under reflection in the y - axis.

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To solve the problem step by step, we will first determine the coordinates of point P before reflection in the y-axis, given its image after reflection in the x-axis. ### Step 1: Understand the reflection in the x-axis When a point (x, y) is reflected in the x-axis, the coordinates of the image become (x, -y). ### Step 2: Identify the coordinates of point P We are given the coordinates of the image after reflection in the x-axis, which are (8, -6). Let’s denote the original point P as (x, y). According to the reflection rule, we can set up the following equations: - x = 8 (the x-coordinate remains the same) - -y = -6 (the y-coordinate changes sign) ### Step 3: Solve for the coordinates of point P From the second equation, we can find the value of y: - -y = -6 - y = 6 Thus, the coordinates of point P are (8, 6). ### Step 4: Reflect point P in the y-axis Now, we need to find the coordinates of the image of point P under reflection in the y-axis. When a point (x, y) is reflected in the y-axis, the coordinates of the image become (-x, y). ### Step 5: Apply the reflection rule Using the coordinates of point P (8, 6): - The x-coordinate will change sign: -8 - The y-coordinate remains the same: 6 Thus, the coordinates of the image of point P under reflection in the y-axis are (-8, 6). ### Final Answer: The coordinates of the image of P under reflection in the y-axis are (-8, 6). ---
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