The coordinates of the vertices of the new triangle will be; (-4, 6), (-5, 3), and (-7, 2)
Please find attached the graph of the image of the triangle after a rotation of 180 degrees about the origin, created with MS Excel.
The steps used to create the attached image are presented as follows;
The coordinates of the vertices of the original triangle are; (4, -6), (5, -3), and (7, -2)
The coordinates of the image of a point (x, y) following a rotation of 180° about the origin produces the point (-x, -y)
Therefore, the coordinates of the image of the vertices of the specified triangle following a rotation of 180° about the origin are;
(4, -6) → Rotation 180° about the origin → (-4, -(6)) = (-4, 6)
(5, -3) → Rotation 180° about the origin → (-5, -(3)) = (-5, 3)
(7, -2) → Rotation 180° about the origin → (-7, -(2)) = (-7, 2)
The above coordinate points can be used to graph the image of the triangle following a rotation of 180 degrees about the origin using MS Excel