Question

#4: the coordinate plane below represents a map, where each unit on the grid represents 10 miles. what is the distance between boca raton and miami?

Explanation:

Step1: Find the coordinates

Assume Boca Raton's coordinate is \((x_1,y_1)=(40,20)\) and Miami's coordinate is \((x_2,y_2)=(40, - 30)\).

Step2: Use the distance formula for points with same \(x\) - coordinate

Since \(x_1 = x_2\), the distance \(d=\vert y_1 - y_2\vert\). Substitute \(y_1 = 20\) and \(y_2=-30\) into the formula: \(d=\vert20-(-30)\vert=\vert20 + 30\vert=\vert50\vert = 50\) units.

Step3: Convert units to miles

Each unit represents \(10\) miles. So the actual distance \(D=50\times10\) miles.

Answer:

\(500\) miles