Question

1. in the following pair of images, △jkl is a scale drawing of △abc.

a. determine the scale factor.
b. write an equation that relates the scale drawing to the original figure. let f represent a length of the original figure, and let d represent the corresponding length of the scale drawing.
c. use the equation to find the length of $overline{jl}$.

Explanation:

Step1: Calculate scale - factor

To find the scale factor, divide the length of a side of the scale - drawing by the length of the corresponding side of the original figure. Let's use sides $AB$ and $JK$. $AB = 2\frac{1}{4}=\frac{9}{4}$ and $JK = 6\frac{3}{4}=\frac{27}{4}$. The scale factor $k=\frac{JK}{AB}=\frac{\frac{27}{4}}{\frac{9}{4}} = 3$.

Step2: Write the relationship equation

The relationship between the length of the original figure $f$ and the length of the scale - drawing $d$ is given by the formula $d=kf$. Since $k = 3$, the equation is $d = 3f$.

Step3: Find length of $\overline{JL}$

We know that the corresponding side in the original figure to $\overline{JL}$ is $\overline{AC}$, and $AC = 3$. Using the equation $d = 3f$, substituting $f = 3$ into the equation, we get $d=3\times3=9$.

Answer:

a. 3
b. $d = 3f$
c. 9