Question

△abc is graphed on a coordinate - plane where a is (1, 4), b is (0, 2), and c is (2, 2). the triangle is dilated by a factor of 2 using a center of dilation at the origin and then the dilation is translated using the rule (x, y)→(x + 4, y - 5). what is the coordinate for b?
a. (-4,9)
b. (0,4)
c. (4,-4)
d. (4,-1)

Explanation:

Step1: Apply dilation rule

The dilation rule for a dilation of factor $k = 2$ with center at the origin $(0,0)$ is $(x,y)\to(kx,ky)$. For point $B(0,2)$, after dilation, $B'=(2\times0,2\times2)=(0,4)$.

Step2: Apply translation rule

The translation rule is $(x,y)\to(x + 4,y - 5)$. For $B'=(0,4)$, we substitute $x = 0$ and $y = 4$ into the translation rule. So, $B''=(0 + 4,4-5)=(4,-1)$.

Answer:

D. $(4,-1)$