Question

a rectangle □abcd has vertices a(0,0), b(4,0), c(4,3), d(0,3). if it is dilated by a scale factor of k = 3, what are the coordinates of b?
a. (12,0)
b. (4,1)
c. (0,12)
dilate △def with vertices d(2,1), e(4,5), f(6,3) by a scale factor k = 2 with the origin as the center of dilation. what are the coordinates of f?
a. (6,12)
b. (3,12)

Explanation:

Step1: Recall dilation formula

When dilating a point $(x,y)$ by a scale - factor $k$ with the origin as the center of dilation, the new coordinates $(x',y')$ are given by $(x',y')=(kx,ky)$.

Step2: Find new coordinates of $B'$

The coordinates of point $B$ are $(4,0)$ and the scale - factor $k = 3$. Using the dilation formula, $x'=k\times x=3\times4 = 12$ and $y'=k\times y=3\times0 = 0$. So the coordinates of $B'$ are $(12,0)$.

Step3: Find new coordinates of $F'$

The coordinates of point $F$ are $(6,3)$ and the scale - factor $k = 2$. Using the dilation formula, $x'=k\times x=2\times6 = 12$ and $y'=k\times y=2\times3 = 6$.

Answer:

1. A. $(12,0)$
2. None of the above. The correct coordinates of $F'$ are $(12,6)$