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: Find scale - factor formula

The scale factor $k$ is the ratio of a length in the scale - drawing to the corresponding length in the original figure. We can use the lengths of corresponding sides. Let's use the sides $AB$ and $JK$. $AB = 2\frac{1}{4}=\frac{9}{4}$ and $JK = 6\frac{3}{4}=\frac{27}{4}$.
$k=\frac{JK}{AB}$

Step2: Calculate the scale factor

$k=\frac{\frac{27}{4}}{\frac{9}{4}}=\frac{27}{4}\times\frac{4}{9}=3$

Step3: Write the relationship equation

The equation relating the length $d$ of the original figure and the length $f$ of the scale - drawing is $f = kd$, where $k = 3$. So the equation is $f = 3d$.

Step4: Find the length of $\overline{JL}$

The corresponding side to $\overline{JL}$ in $\triangle ABC$ is $\overline{AC}$. $\overline{AC}=3$. Using the equation $f = 3d$, when $d = 3$, $f=3\times3 = 9$.

Answer:

a. The scale factor is 3.
b. The equation is $f = 3d$.
c. The length of $\overline{JL}$ is 9.