Question

1. in the following pair of images, △jkl is a scale drawing of △abc. (△abc has sides: (ac = 3), (bc = 2), (ab = 2\frac{1}{4}); △jkl has sides: (jk = 6\frac{3}{4}), (kl = 6), (jl) (unknown))

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:

Part a: Determine the scale factor

Step 1: Identify corresponding sides

We know that $\triangle JKL$ is a scale drawing of $\triangle ABC$. Let's take the corresponding sides $AB$ and $JK$. The length of $AB = 2\frac{1}{4}=\frac{9}{4}$ and the length of $JK = 6\frac{3}{4}=\frac{27}{4}$.

Step 2: Calculate the scale factor

The scale factor $k$ is the ratio of the length of the scale drawing side to the original figure side. So $k=\frac{JK}{AB}=\frac{\frac{27}{4}}{\frac{9}{4}}$.

When dividing fractions, we multiply by the reciprocal: $\frac{27}{4}\times\frac{4}{9} = 3$.

Step 1: Define variables

Let $f$ be the length of the original figure and $d$ be the length of the scale drawing.

Step 2: Relate using scale factor

Since the scale factor is $3$, the length of the scale drawing $d$ is $3$ times the length of the original figure $f$. So the equation is $d = 3f$.

Step 1: Identify corresponding side

The corresponding side of $\overline{JL}$ in the original figure is $\overline{AC}$. The length of $\overline{AC}=3$.

Step 2: Use the equation

From part (b), we have $d = 3f$. Here, $f = 3$ (length of $\overline{AC}$), so we substitute $f = 3$ into the equation: $d=3\times3 = 9$.

Answer:

The scale factor is $3$.

Part b: Write an equation relating scale drawing and original figure