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 scale - factor formula

The scale factor $k$ for dilation of a point $(x,y)$ to $(x',y')$ is given by $k=\frac{x'}{x}=\frac{y'}{y}$ (assuming $x
eq0$ and $y
eq0$).

Step2: Calculate scale - factor for point J

For point $J:(2,4)\to J'(4,8)$, using the $x$ - coordinates, $k=\frac{x_{J'}}{x_J}=\frac{4}{2} = 2$. Using the $y$ - coordinates, $k=\frac{y_{J'}}{y_J}=\frac{8}{4}=2$.

Step3: Calculate scale - factor for point K

For point $K:(1,1)\to K'(2,2)$, using the $x$ - coordinates, $k=\frac{x_{K'}}{x_K}=\frac{2}{1}=2$. Using the $y$ - coordinates, $k=\frac{y_{K'}}{y_K}=\frac{2}{1}=2$.

Step4: Calculate scale - factor for point L

For point $L:(4,0)\to L'(8,0)$, using the $x$ - coordinates, $k=\frac{x_{L'}}{x_L}=\frac{8}{4}=2$. Since $y = 0$ for point $L$, we rely on the $x$ - coordinate calculation.

Answer:

D. 2