Question

question. the figure below is dilated with the center of dilation at the origin and a scale factor of 1/2 and then rotated 180° clockwise. what are the coordinates of the image of point t after these transformations?

Explanation:

Step1: Determine original coordinates

From the graph, the coordinates of point T are $(2, - 1)$.

Step2: Perform dilation

For dilation with a scale - factor of $\frac{1}{2}$ centered at the origin, we use the rule $(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$. So, $(2,-1)\to(2\times\frac{1}{2},-1\times\frac{1}{2})=(1,-\frac{1}{2})$.

Step3: Perform rotation

For a $180^{\circ}$ clock - wise rotation about the origin, we use the rule $(x,y)\to(-x,-y)$. So, $(1,-\frac{1}{2})\to(-1,\frac{1}{2})$.

Answer:

$(-1,\frac{1}{2})$