Question

similarity transformations cfu
find the vertices of the image of $\triangle abc$ after a dilation centered at the origin with scale factor of 2. then, translate $\triangle abc$ under the rule $(x, y) \to (x - 3, y + 1)$

$a(1, 0)$ $b(3, -1)$ $c(4, 1)$
check the dilation

Explanation:

Step1: Dilate each vertex by scale 2

For a dilation centered at the origin with scale factor $k$, the transformation is $(x,y)\to(kx,ky)$.

• $A'(1\times2, 0\times2)=(2,0)$
• $B'(3\times2, -1\times2)=(6,-2)$
• $C'(4\times2, 1\times2)=(8,2)$

Step2: Translate each dilated vertex

Use the translation rule $(x,y)\to(x-3,y+1)$:

• $A''(2-3, 0+1)=(-1,1)$
• $B''(6-3, -2+1)=(3,-1)$
• $C''(8-3, 2+1)=(5,3)$

Answer:

Vertices of the final image: $A''(-1, 1)$, $B''(3, -1)$, $C''(5, 3)$