Final Answer:
Alana correctly reflected triangle ABC across the x-axis to form triangle A’B’C’. However, there is a mistake in the dilation step. The correct dilated image, A”B”C”, should be formed by multiplying the coordinates of A’, B’, and C’ by the scale factor of 2.
Step-by-step explanation:
Alana's work in reflecting triangle ABC across the x-axis is accurate, resulting in the formation of triangle A’B’C’. However, the mistake occurs in the dilation step.
When dilating an image by a scale factor of 2 with the center of dilation at the origin, each coordinate (x, y) should be multiplied by the scale factor. In this case, Alana should have multiplied the coordinates of A’, B’, and C’ by 2 to obtain the correct dilated image, A”B”C”.
Let's delve into the correction process. If the coordinates of A’B’C’ are (x1, y1), (x2, y2), and (x3, y3), then the correct coordinates for A”B”C” can be found by multiplying each coordinate by 2.
Therefore, the corrected coordinates for A”B”C” are (2x1, 2y1), (2x2, 2y2), and (2x3, 2y3). This ensures that each point is dilated outward from the origin by a factor of 2.
In summary, Alana's reflection was accurate, but the mistake lies in the dilation step. Correcting this involves multiplying the coordinates of A’B’C’ by the scale factor of 2 to obtain the correct dilated image, A”B”C”.