Question

1. error analysis kendall was asked to find the scale factor for the dilation. what is kendalls error?

the original rectangle has length 6 (from b to c) and height 2 (from b to a). the dilated rectangle has length 3 (from b to c) and height 1 (from b to a).
kendalls calculation: \\(\frac{6}{2} = 3\\)
the scale factor is 3 (marked with an x)

Explanation:

Step1: Recall scale factor definition

Scale factor = $\frac{\text{Image length}}{\text{Pre-image length}}$

Step2: Identify correct length pairs

Pre-image side $BC=6$, image side $B'C'=3$; or pre-image $AB=2$, image $A'B'=1$.

Step3: Calculate correct scale factor

$\text{Scale factor} = \frac{3}{6} = \frac{1}{2}$ (or $\frac{1}{2}$ from $\frac{1}{2}$)

Step4: Identify Kendall's error

Kendall used $\frac{\text{Pre-image length}}{\text{Image length}}$ instead of the correct ratio.

Answer:

Kendall calculated the scale factor as the ratio of the pre-image length to the image length (using $\frac{6}{2}=3$) instead of the correct ratio of image length to pre-image length. The correct scale factor is $\frac{1}{2}$.