Triangle \( A B C \) has its vertices at points \( A(5,5), B(2,8) \), and \( C(9,7) \). If the triangle is reflected across the line \( y=3 \), find the coordinates of \( C \). Select one: a. \( (9,1) \) b. \( (7,-1) \) c. \( (9,-1) \) d. \( (-2,-1) \)
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To find the coordinates of point \( C(9,7) \) after reflecting across the line \( y=3 \), we first determine the vertical distance from point \( C \) to the line \( y=3 \). The y-coordinate of \( C \) is 7, and the line \( y=3 \) is 4 units below \( C \) (since \( 7 - 3 = 4 \)). When reflecting across a line, the distance from the point to the line on one side will be the same on the other side. Therefore, we subtract this distance from the line \( y=3 \): \[ 3 - 4 = -1 \] So, the reflected coordinates of point \( C \) are \( (9, -1) \). Thus, the correct answer is: c. \( (9,-1) \)
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