Final answer:
To rotate triangle ABC with vertices A(0,0), B(2,4), and C(3,0) 180 degrees about the origin, you negate the x and y coordinates resulting in A'(0,0), B'(-2,-4), and C'(-3,0).
Step-by-step explanation:
To rotate the triangle ABC with vertices A(0,0), B(2,4), and C(3,0) about the origin by 180 degrees, we apply a rotation transformation. The general rule for a 180-degree rotation in the coordinate plane is to change the sign of both the x and y coordinates of each point. Therefore:
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- The coordinates of point A after rotation will be (0,0), as it is on the origin.
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- The coordinates of point B after rotation will become B'(-2,-4).
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- The coordinates of point C after rotation will become C'(-3,0).
The transformed triangle A'B'C' will be the image of triangle ABC after a 180-degree rotation about the origin.