Question

The vertices of a triangle are A (2, 5), B(1, 2), and C (3, 1). Find the coordinates of the image after a

dilation with respect to the origin using a scale factor of 2 and then a translation 2 units left and 1 unit up.
A'(
B'(
C'(_
Is AABC congruent to AA'B'C'? Yes or No.
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Answer 1

To find the image of a triangle after a dilation with respect to the origin and a translation, apply the transformations to each vertex. The triangles AABC and AA'B'C' are not congruent.

Step-by-step explanation:

To find the image of a triangle after a dilation with respect to the origin using a scale factor of 2 and then a translation 2 units left and 1 unit up, we need to apply these transformations to each vertex of the triangle.

First, let's apply the dilation with respect to the origin using a scale factor of 2. To do this, we multiply the x and y coordinates of each vertex by 2. So, the new coordinates of A', B', and C' after the dilation would be:

A'(-4, 10), B'(-2, 4), C'(6, 2).

Next, let's apply the translation 2 units left and 1 unit up to each vertex. To do this, we subtract 2 from the x-coordinate and subtract 1 from the y-coordinate. So, the final coordinates of A', B', and C' after both transformations would be:

A'(-6, 9), B'(-4, 3), C'(4, 1).

The triangles AABC and AA'B'C' are not congruent because the corresponding sides and angles of the two triangles are not equal.

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