Question

problem #3 - unit 2 (mild)
example 3: john dilated the δabc by a scale factor of 3 to obtain the image triangle δabc. the coordinates of the vertices of δabc are: a(3,3), b(5,3), c(5,1). determine the coordinates of δabc.
a (__, ) b (, ) c (, __)

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated by a scale - factor $k$ with the center of dilation at the origin, the new coordinates $(x',y')$ are given by $(kx,ky)$. Here, $k = 3$.

Step2: Calculate coordinates of $A'$

For point $A(3,3)$, $x = 3,y = 3$. Then $x'=3\times3 = 9$ and $y'=3\times3 = 9$. So $A'(9,9)$.

Step3: Calculate coordinates of $B'$

For point $B(5,3)$, $x = 5,y = 3$. Then $x'=3\times5 = 15$ and $y'=3\times3 = 9$. So $B'(15,9)$.

Step4: Calculate coordinates of $C'$

For point $C(5,1)$, $x = 5,y = 1$. Then $x'=3\times5 = 15$ and $y'=3\times1 = 3$. So $C'(15,3)$.

Answer:

$A'(9,9)$, $B'(15,9)$, $C'(15,3)$