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 jl.

Explanation:

Step1: Calculate scale - factor

The scale factor $k$ is found by dividing a side - length of the scaled figure by the corresponding side - length of the original figure. Let's use the sides $AB$ and $JK$. $AB = 2\frac{1}{4}=\frac{9}{4}$ and $JK = 6\frac{3}{4}=\frac{27}{4}$. Then $k=\frac{JK}{AB}=\frac{\frac{27}{4}}{\frac{9}{4}} = 3$.

Step2: Write the equation

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

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

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

Answer:

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