Leslie was able to map \overline{ST} ST start overline, S, T, end overline onto \overline{QR} QR start overline, Q, R, end overline using a rotation and dilation. Leslie concluded: "I was able to map \overline{ST} ST start overline, S, T, end overline onto \overline{QR} QR start overline, Q, R, end overline using a sequence of rigid transformations, so the figures are congruent." What error did Leslie make in her conclusion?

The fact that Leslie used a dilation is where she made the mistake. A dilation either shrinks or enlarges a figure. So it made segment ST either larger or smaller to be able to fit to segment QR.

But congruent segments are always the same length. So there's no way that a dilation can be involved. Only rigid transformations of translations (aka shifting), reflections, and rotations are allowed. A dilation is not a rigid transformation.

a

explanation:

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)