QuestionA triangle with vertices $A(0,0), B(2,0), C(0,4)$ is rotated $180^{\circ}$ and dilated by 3. Find new coordinates and similarity/congruence.

Studdy Solution
Since the transformed triangle is a dilation of the original triangle with a scale factor not equal to1, the two triangles are similar but not congruent.
The coordinates of $\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$ are $A^{\prime \prime}(0,0), B^{\prime \prime}(-6,0)$, and $C^{\prime \prime}(0,-12)$. $\triangle A B C \sim \triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$ because a dilation with a scale factor that is not equal to1 produces an image that is similar, but not congruent, to the original figure.