find the image of S(-1,-3) after a reflection scross the line y=-2
The best way to do this is to actually sketch it.
I am sure it will make perfect sense to you after you draw it.
Remember that y =-2 is a horizontal line 2 units below the x-axis
the image is the same distance above the line y = -2 as it was below it to start. So,
y -> -2+(-2-y) = -2+(y+4) = y+2
(-1,-3) -> (-1,-1)
To find the image of a point after a reflection across a line, you can follow these steps:
1. Determine the equation of the line of reflection. In this case, the line of reflection is y = -2.
2. Find the distance between the given point S(-1, -3) and the line of reflection y = -2. To do this, you need to find the perpendicular distance from the point to the line. Since the line is horizontal, the distance between the point and the line is the difference between the y-coordinates.
Distance = |-3 - (-2)| = |-3 + 2| = 1.
3. Add twice the distance to the y-coordinate of the line of reflection to find the image point. Since the displacement is perpendicular to the line of reflection, the x-coordinate remains the same.
New y-coordinate = -2 + (2 * Distance) = -2 + (2 * 1) = -2 + 2 = 0.
Therefore, the image of S(-1, -3) after reflection across the line y = -2 is (-1, 0).
So, the image point after the reflection across the line y = -2 is (-1, 0).