Question

the vertices of a figure are given. what are the coordinates of the image after the given dilation? identify the type of dilation. m(2,3), n(5,3), p(5,1) k = 3

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ and a dilation factor $k$, the new - point $(x',y')$ after dilation is given by $(x',y')=(kx,ky)$.

Step2: Find the coordinates of $M'$

Given $M(2,3)$ and $k = 3$.
$x_M=2,y_M = 3$. Then $x_{M'}=k\times x_M=3\times2 = 6$ and $y_{M'}=k\times y_M=3\times3 = 9$. So $M'(6,9)$.

Step3: Find the coordinates of $N'$

Given $N(5,3)$ and $k = 3$.
$x_N=5,y_N = 3$. Then $x_{N'}=k\times x_N=3\times5 = 15$ and $y_{N'}=k\times y_N=3\times3 = 9$. So $N'(15,9)$.

Step4: Find the coordinates of $P'$

Given $P(5,1)$ and $k = 3$.
$x_P=5,y_P = 1$. Then $x_{P'}=k\times x_P=3\times5 = 15$ and $y_{P'}=k\times y_P=3\times1 = 3$. So $P'(15,3)$.

Step5: Identify the type of dilation

Since $k = 3>1$, the dilation is an enlargement.

Answer:

$M'(6,9)$
$N'(15,9)$
$P'(15,3)$
Type of dilation: Enlargement