Question

the figure below is rotated 180° clockwise and then dilated with the center of dilation at the origin and a scale factor of $\frac{1}{2}$. what are the coordinates of the image of point e after these transformations?

Explanation:

Step1: Determine the coordinates of point E

The coordinates of point E are $(-5,2)$.

Step2: Apply the 180 - degree clockwise rotation

The rule for a 180 - degree clockwise rotation about the origin is $(x,y)\to(-x,-y)$. For point E$(-5,2)$, after rotation, the coordinates become $(5, - 2)$.

Step3: Apply the dilation

The rule for dilation with a center at the origin and a scale factor $k=\frac{1}{2}$ is $(x,y)\to(kx,ky)$. For the point $(5,-2)$ after dilation, we have $x = 5\times\frac{1}{2}=\frac{5}{2}$ and $y=-2\times\frac{1}{2}=-1$.

Answer:

$(\frac{5}{2},-1)$