Question

problem 4 a map of colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. are these two ways of reporting the scale the same? explain your reasoning. problem 5 here is a polygon on a grid. a. draw a scaled copy of the polygon using a scale factor of 3. label the copy a. b. constant of proportionality: equation: c =

Explanation:

Problem 4

The first scale 1 inch to 20 miles can be written as the ratio 1:20. The second scale 1 to 1,267,200 means 1 unit on the map to 1,267,200 of the same - type units in real - life. Since 1 mile = 63360 inches, 20 miles = 20×63360 = 1267200 inches. So both scales represent the same relationship between map and real - life distances.

Step1: Multiply x - coordinates

For each vertex of the original polygon, multiply the x - coordinate by the scale factor 3.

Step2: Multiply y - coordinates

Multiply the y - coordinate of each vertex of the original polygon by the scale factor 3.

Step3: Plot new points

Plot the new points on the grid and connect them to form the scaled - copy polygon A.

Step1: Find the constant of proportionality

The constant of proportionality $k$ in a direct - proportion $y = kx$ can be found by dividing $y$ by $x$. For example, when $x = 10$ and $y=31.4$, $k=\frac{31.4}{10}=3.14$. Check for other pairs: $\frac{15.7}{5}=3.14$, $\frac{9.42}{3}=3.14$, $\frac{6.28}{2}=3.14$.

Step2: Write the equation

The equation for the direct - proportion is $C = 3.14d$.

Answer:

Yes, the two ways of reporting the scale are the same.

Problem 5