Question

A triangle has vertices at F (6, 3), G (3, 4), and H (1, 7). What are the coordinates of each vertex if the triangle is rotated 180° about the origin counterclockwise?

1. thuthao
To rotate a triangle 180° about the origin counterclockwise, we can take each vertex of the triangle and reflect it across the origin. This will produce a new set of coordinates for each vertex that is the same distance from the origin as the original, but on the opposite side of the origin.
For example, the vertex F has coordinates (6, 3). If we reflect this point across the origin, we get the new point (-6, -3). Similarly, the vertex G has coordinates (3, 4), which become (-3, -4) when reflected across the origin, and the vertex H has coordinates (1, 7), which become (-1, -7) when reflected across the origin.
Therefore, the coordinates of each vertex of the triangle after rotating it 180° about the origin counterclockwise are as follows:
• F: (-6, -3)
• G: (-3, -4)
• H: (-1, -7)
Note: When rotating a point about the origin, the direction of rotation (clockwise or counterclockwise) is important. If we had rotated the triangle 180° about the origin clockwise instead of counterclockwise, the new coordinates of each vertex would have been the same as the original, since the triangle would be reflected across the origin and end up in the same position as it started.