Question

in the following pair of shapes. △abc is a scale - drawing of △jkl.

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: Identify corresponding sides

Let's assume side $AB = 2\frac{1}{2}=\frac{5}{2}$ in the scale - drawing corresponds to side $JK = 6\frac{1}{4}=\frac{25}{4}$ in the original figure.

Step2: Calculate the scale factor

The scale factor $k$ is the ratio of the length in the scale - drawing to the length in the original figure. So $k=\frac{d}{f}$, where $d$ is the length in the scale - drawing and $f$ is the length in the original figure. $k=\frac{\frac{5}{2}}{\frac{25}{4}}=\frac{5}{2}\times\frac{4}{25}=\frac{2}{5}$.

Step3: Write the equation

The equation that relates the scale drawing to the original figure is $d = kf$, substituting $k=\frac{2}{5}$, we get $d=\frac{2}{5}f$.

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

If we assume the side corresponding to $\overline{JL}$ in the scale - drawing has length $d$ and we know the scale factor $k = \frac{2}{5}$. Let's say the length of $\overline{JL}$ in the original figure is $f = 6$. Then $d=\frac{2}{5}\times6=\frac{12}{5}=2.4$.

Answer:

a. The scale factor is $\frac{2}{5}$.
b. The equation is $d=\frac{2}{5}f$.
c. If the original length is 6, the length in the scale - drawing is 2.4.