Reflect \( A=(5,3) \quad B=(8,5) \) over \( y=-2 \)

To reflect a point over a line, we need to find the perpendicular line to the given line that passes through the point, and then find the intersection point of these two lines. Given points: \( A = (5, 3) \) \( B = (8, 5) \) Given line: \( y = -2 \) To reflect a point over a line, we need to find the perpendicular line to the given line that passes through the point, and then find the intersection point of these two lines. Let's find the equation of the perpendicular line to \( y = -2 \) that passes through point \( A = (5, 3) \). The slope of the perpendicular line is the negative reciprocal of the slope of the given line. Since the given line is horizontal, its slope is 0. Therefore, the slope of the perpendicular line is undefined, which means it is a vertical line. The equation of the vertical line passing through point \( A = (5, 3) \) is \( x = 5 \). Now, we need to find the intersection point of the vertical line \( x = 5 \) and the given line \( y = -2 \). At the intersection point, the x-coordinate is 5 and the y-coordinate is -2. Therefore, the reflected point of \( A = (5, 3) \) over \( y = -2 \) is \( (5, -2) \). Similarly, we can find the reflected point of \( B = (8, 5) \) over \( y = -2 \) by following the same process. Let's calculate the reflected points for both \( A \) and \( B \). Calculate the value by following steps: - step0: Calculate: \(5.3+0.4\) - step1: Add the numbers: \(5.7\) The reflected point of \( A = (5, 3) \) over \( y = -2 \) is \( (5, -2) \). Now, let's calculate the reflected point of \( B = (8, 5) \) over \( y = -2 \). Calculate the value by following steps: - step0: Calculate: \(8.5+0.4\) - step1: Add the numbers: \(8.9\) The reflected point of \( B = (8, 5) \) over \( y = -2 \) is \( (8, -2) \). Therefore, the reflected points of \( A \) and \( B \) over \( y = -2 \) are \( (5, -2) \) and \( (8, -2) \) respectively.