Question

using the following dilated coordinates of a triangle choose the appropriate scale factor. j:(2,4)→j(4,8) k:(1,1)→k(2,2) l:(4,0)→l(8,0) a 5 b 4 c 3 d 2

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated about the origin with scale - factor $k$, the new point is $(kx,ky)$.

Step2: Find scale - factor for point J

For point $J(2,4)$ which dilates to $J'(4,8)$. Let the scale - factor be $k$. Then $kx = 4$ and $ky = 8$ where $x = 2$ and $y = 4$. Substituting $x = 2$ into $kx=4$, we get $k\times2 = 4$, so $k = 2$.

Step3: Check for other points

For point $K(1,1)$ which dilates to $K'(2,2)$. Using the formula $(kx,ky)$, when $x = 1$ and $y = 1$, if $k = 2$, then $(k\times1,k\times1)=(2,2)$. For point $L(4,0)$ which dilates to $L'(8,0)$. When $x = 4$ and $y = 0$, if $k = 2$, then $(k\times4,k\times0)=(8,0)$.

Answer:

A. 2