The image of the point (1, -2) after a rotation of 180° about the origin is
To find the image of a point after a rotation, we need to follow a few steps:
Step 1: Determine the coordinates of the point before the rotation. In this case, the point is (1, -2).
Step 2: Apply the rotation formula. A rotation of 180 degrees about the origin can be achieved by multiplying the coordinates of the point by the matrix below:
| -1 0 |
| 0 -1 |
Step 3: Multiply the coordinates of the point by the rotation matrix. Let's call the original point (x, y) and the rotated point (x', y'). Applying the rotation formula, we have:
x' = (-1)(x) + (0)(y) = -x
y' = (0)(x) + (-1)(y) = -y
Using the given point (1, -2), we can substitute the values into the rotation formula as follows:
x' = -1(1) = -1
y' = -1(-2) = 2
Therefore, the image of the point (1, -2) after a rotation of 180° about the origin is (-1, 2).