With the image of O(-2,-1) after 2 reflections. one across the line y=-5 and line x=1
refelection about y=-5
distance from that line is 4, so new y is -9
now reflection about x=1
distance from that line is 3, so new O is
4,-9
classifying triangles
To find the image of a point after reflections, you can follow these steps:
Step 1: Perform the first reflection across the line y = -5.
To reflect a point across a horizontal line, such as y = -5, the x-coordinate remains the same, and the y-coordinate changes sign. Therefore, to reflect the point O(-2, -1) across y = -5, the new coordinates will be O'(-2, -1) → (-2, 1).
Step 2: Perform the second reflection across the line x = 1.
To reflect a point across a vertical line, such as x = 1, the y-coordinate remains the same, and the x-coordinate changes sign. So, to reflect the point O'(-2, 1) across x = 1, the new coordinates will be O''(2, 1).
Therefore, the image of the point O(-2, -1) after two reflections (first across y = -5 and then across x = 1) is O''(2, 1).