Question

identify the preimage of the figure, then perform the dilation according to the given scale factor (k). a(5,), b(5,1), c(0,0), k = 2, a(10,), b(10,2), c(0,0)

Explanation:

Step1: Recall dilation rule

For a dilation with scale - factor $k$ centered at the origin $(0,0)$, if a point $(x,y)$ is dilated, the new point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Find the $y$ - coordinate of $A'$

The coordinates of point $A$ are $(5, - 1)$ and the scale - factor $k = 2$. Using the dilation formula $y'=k\cdot y$, we substitute $k = 2$ and $y=-1$. So $y'=2\times(-1)=-2$.

Answer:

$A'(10,-2)$