Question

damian dilates PQR shown on the coordinate grid with a scale factor of 0.5 centered at the origin. then he translate the 1 unit up and 3 units to the right to from P' Q' R' what are the coordinates of the vertices P' Q' R'

Answer 1

Transformation involves changing the size and position of a shape.

The coordinates of P'Q'R' follows the transformation rule $\mathbf{(x,y) \to (0.5x-3,0.5y+1)}$

First PQR is dilated by 0.5.

The transformation rule of this dilation is:

$\mathbf{(x,y) \to 0.5(x,y)}$

This gives

$\mathbf{(x,y) \to (0.5x,0.5y)}$

Next, the points are translated 1 unit up and 3 units right.

The transformation rule of this translation is:

$\mathbf{(x,y) \to (x-3,y+1)}$

So, we have:

$\mathbf{(x,y) \to (0.5x-3,0.5y+1)}$

Hence, the coordinates of P'Q'R' follows the transformation rule $\mathbf{(x,y) \to (0.5x-3,0.5y+1)}$

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