Help! I have to graph my answer to this problem: ADFG has vertices D (–2, 4), F (–3,1), and G (–1, 2). Find the vertices of the image after the rotation of 180° about the origin.
after a 180° rotation
(x,y) ----> (-x,-y)
so
D(-2,4) -----> D'(2,-4)
same for the other points,
it is really that easy.
To find the vertices of the image after a rotation of 180° about the origin, you can use the following steps:
1. Plot the original points on a coordinate plane. In this case, plot point D at (-2, 4), point F at (-3, 1), and point G at (-1, 2).
2. To rotate a point (x, y) 180° about the origin, you need to negate both the x and y coordinates. So, for each point, apply this transformation.
- For point D: Negate the x-coordinate and the y-coordinate. So, D' = (-(-2), -(4)) = (2, -4).
- For point F: Negate the x-coordinate and the y-coordinate. So, F' = (-(-3), -(1)) = (3, -1).
- For point G: Negate the x-coordinate and the y-coordinate. So, G' = (-(-1), -(2)) = (1, -2).
3. Plot the new points obtained after the rotation. In this case, plot point D' at (2, -4), point F' at (3, -1), and point G' at (1, -2).
4. Connect the new points to form a rotated image. In this case, connect D' to F', F' to G', and G' back to D'. This will form the rotated image of ADFG after a rotation of 180° about the origin.
This is how you can graph the answer to the problem.