Question

the scale factor is 4, and the center of dilation is the origin. what are the coordinates of a, b, and c a = ( , ) b = ( , ) c = ( , )

Explanation:

Step1: Recall the dilation formula

If the scale factor is $k = 4$ and the center of dilation is the origin $(0,0)$, and a point $P=(x,y)$ is dilated to $P'=(x',y')$, then the formula is $x'=k\times x$ and $y'=k\times y$.

Step2: Find the coordinates of $A$

Assume the original point $A=(1,4)$. Using the dilation formula:
For the $x$ - coordinate of $A'$: $x'=4\times1 = 4$
For the $y$ - coordinate of $A'$: $y'=4\times4=16$. So $A'=(4,16)$

Step3: Find the coordinates of $B$

Assume the original point $B=(3,1)$. Using the dilation formula:
For the $x$ - coordinate of $B'$: $x'=4\times3 = 12$
For the $y$ - coordinate of $B'$: $y'=4\times1 = 4$. So $B'=(12,4)$

Step4: Find the coordinates of $C$

Assume the original point $C=(1,1)$. Using the dilation formula:
For the $x$ - coordinate of $C'$: $x'=4\times1=4$
For the $y$ - coordinate of $C'$: $y'=4\times1 = 4$. So $C'=(4,4)$

Answer:

$A'=(4,16)$, $B'=(12,4)$, $C'=(4,4)$