(1) Reflect \( A=(5,3) B=(8,5) \) over \( y=-2 \) (2) Point \( A(3,5) \) is translated 4 units to the right

Let's solve each part step by step. ### (1) Reflect \( A=(5,3) \) and \( B=(8,5) \) over the line \( y=-2 \) To reflect a point over a horizontal line, we can use the following formula: If a point \( (x, y) \) is reflected over the line \( y = k \), the new point \( (x', y') \) can be calculated as: \[ y' = k - (y - k) = 2k - y \] In this case, \( k = -2 \). **Reflecting point A:** - Original point \( A = (5, 3) \) - Calculate the new y-coordinate: \[ y' = -2 - (3 - (-2)) = -2 - (3 + 2) = -2 - 5 = -7 \] - The x-coordinate remains the same: \[ A' = (5, -7) \] **Reflecting point B:** - Original point \( B = (8, 5) \) - Calculate the new y-coordinate: \[ y' = -2 - (5 - (-2)) = -2 - (5 + 2) = -2 - 7 = -9 \] - The x-coordinate remains the same: \[ B' = (8, -9) \] So, the reflected points are: - \( A' = (5, -7) \) - \( B' = (8, -9) \) ### (2) Translate point \( A(3,5) \) 4 units to the right To translate a point \( (x, y) \) to the right by \( d \) units, we simply add \( d \) to the x-coordinate: \[ (x', y') = (x + d, y) \] In this case, \( d = 4 \) and the original point is \( A(3, 5) \). Calculating the new coordinates: \[ x' = 3 + 4 = 7 \] \[ y' = 5 \] So, the new point after translation is: - \( A' = (7, 5) \) ### Summary of Results 1. Reflected points: - \( A' = (5, -7) \) - \( B' = (8, -9) \) 2. Translated point: - \( A' = (7, 5) \)