Question

Which transformations could be performed to show that △ABC is similar to △A ′′B ′′C '′?

a) A reflection over the x-axis, then a dilation by a scale factor of 3.
b) A reflection over the x-axis, then a dilation by a scale factor of -6.
c) A 180° rotation about the origin, then a dilation by a scale factor of 3.
d) A 180° rotation about the origin, then a dilation by a scale factor of -10.

Answer 1

The transformations that could be performed are a reflection over the x-axis followed by a dilation by different scale factors or a rotation of 180° followed by a dilation.

Step-by-step explanation:

The transformations that could be performed to show that triangle ABC is similar to triangle A''B''C' are:

a) A reflection over the x-axis, then a dilation by a scale factor of 3.

b) A reflection over the x-axis, then a dilation by a scale factor of -6.

c) A 180° rotation about the origin, then a dilation by a scale factor of 3.

d) A 180° rotation about the origin, then a dilation by a scale factor of -10.

These transformations change the position, orientation, and size of the triangles while preserving their shape, making them similar.