Question

An isosceles triangle is transformed such that the vertex P' corresponds to the vertex P. Which statement describes the transformation of the triangle? The triangle was reflected over the y-axis. The triangle was translated to the right 8 units. The triangle was dilated. The triangle was rotated 180 counterclockwise.

Answer 1

If an isosceles triangle is transformed such that the vertex P' corresponds to the vertex P, then the transformation that has taken place is a reflection over the line of symmetry that bisects the base of the isosceles triangle. Therefore, the correct statement that describes the transformation of the triangle is "the triangle was reflected over the line of symmetry that bisects its base."

So, the statement "the triangle was reflected over the y-axis" is incorrect, because the line of symmetry of the isosceles triangle is not necessarily the y-axis. The statement "the triangle was translated to the right 8 units" is also incorrect, because translation does not change the shape or orientation of the triangle. The statement "the triangle was dilated" is also incorrect, because dilation would change the size of the triangle, but not necessarily its shape or orientation. Finally, the statement "the triangle was rotated 180 counterclockwise" is also incorrect, because this transformation would place the vertex P' opposite to the original vertex P, rather than corresponding to it.