Question

7. Marco was asked to rotate thecoordinate P(3,-4) 180 degrees about theorigin. Then, he decided to perform atranslation of (x, y+2) followed by adilation of 2. Marco was convinced thatP and P'" had the same coordinates. IsMarco correct? Explain your reasoning.

Answer 1

Let's take this, step by step.

First step:

Rotate the coordinate 180 degrees about the origin.

When a 180 degrees rotation about the origin is performed the coordinates (x, y) changes to (-x, -y)

Thus, P(3, -4) changes to P'(-3, 4)

Second Step:

Perform a translation of (x, y+2)

P'(-3,4) = P''(-3, 4+2) = P''(-3, 6)

Third step:

Perform a dilation of 2.

P''(-3, 6) = P'''(-3*2, 6*2) = P'''(-6, 12)

We can see that,

P(3, -4) while P'''(-6, 12)

Therefore, P and P''' do not have the same coordinates