Question

a hexagon is graphed on a coordinate grid and then dilated by a scale factor of a with the origin as the center of dilation. if a vertex of the original hexagon was located at (-10, 4), which ordered pair represents the vertex of the new hexagon after the dilation? (-10a, 4a) (\frac{-10}{a}, \frac{4}{a}) (-10 + a, 4 + a) (-10+\frac{1}{a},4 + \frac{1}{a})

Explanation:

Step1: Recall dilation rule

When a point $(x,y)$ is dilated by a scale - factor $a$ with the origin $(0,0)$ as the center of dilation, the new coordinates $(x',y')$ are given by the formula $x' = ax$ and $y'=ay$.

Step2: Apply the rule to the given point

The original point is $(-10,4)$. Here $x=-10$ and $y = 4$. After dilation by a scale - factor $a$, the new $x$ - coordinate is $x'=-10a$ and the new $y$ - coordinate is $y' = 4a$.

Answer:

$(-10a,4a)$