What are the coordinates of point A’, the image of A (3, -2), after a reflection over the line y=x+3?
To find the coordinates of point A' after a reflection over the line y=x+3, you need to follow these steps:
1. Plot the line y=x+3 on a coordinate plane. This line has a slope of 1 and a y-intercept (when x=0) of 3. So you can start by plotting the point (0, 3) and then finding other points on the line by moving one unit up and one unit to the right.
2. Plot the point A(3, -2) on the same coordinate plane.
3. Draw a line segment connecting point A and the line y=x+3. This line segment will be perpendicular to the line y=x+3.
4. Extend the line segment on the other side of the line. The point where the extended line segment intersects the line y=x+3 is point A'.
5. Determine the coordinates of A' by finding the intersection point. The coordinates of point A' will be the coordinates of the intersection point.
By following these steps, you can calculate the coordinates of point A' after the reflection.