Question

15 multiple choice 1 point
△ghj with vertices g(-2, 4), h(3, 6) and j(3, -2) is dilated by a factor of $\frac{1}{3}$. in the image △ghj, what are the coordinates of j?
△ghj con los vértices g(-2, 4), h(3, 6) y j(3, -2) se dilata por un factor o $\frac{1}{3}$. en la imagen △ghj, ¿cuáles son las coordenadas de j?
(1, $-\frac{2}{3}$)
(1, 2)
($-\frac{7}{3}$, $\frac{13}{3}$)
($-\frac{2}{3}$, $\frac{4}{3}$)
clear my selection

Explanation:

Step1: Recall dilation formula

When a point $(x,y)$ is dilated by a scale - factor $k$ with the origin as the center of dilation, the new coordinates $(x',y')$ are given by $(x',y')=(kx,ky)$. Here, $k = \frac{1}{3}$, and the point $J$ has coordinates $(x = 3,y=-2)$.

Step2: Calculate the new $x$-coordinate

$x'=k\times x=\frac{1}{3}\times3 = 1$

Step3: Calculate the new $y$-coordinate

$y'=k\times y=\frac{1}{3}\times(-2)=-\frac{2}{3}$

Answer:

$(1,-\frac{2}{3})$