Question

5 ms. dolphin left her home, with coordinates (5, 2), and drove to the library at coordinates (5, -3). then drove to the acme with coordinates (-5, -3). if each unit represents 1 mile, what was the total distance (in miles) that ms. dolphin drove? how far is (5,2) from (5, -3)? how far is (5, -3) from (-5, -3)? add those distances together to determine the total number of miles walked.

Explanation:

Step1: Calculate the distance from \((5,2)\) to \((5, - 3)\)

The \(x -\)coordinates are the same (\(x = 5\)). Use the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(x_1=x_2\): \(d=\vert y_1 - y_2\vert\). Here, \(y_1 = 2\), \(y_2=-3\), so \(d_1=\vert2-(-3)\vert=\vert2 + 3\vert=5\).

Step2: Calculate the distance from \((5,-3)\) to \((-5,-3)\)

The \(y -\)coordinates are the same (\(y=-3\)). Use the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(y_1 = y_2\): \(d=\vert x_1 - x_2\vert\). Here, \(x_1 = 5\), \(x_2=-5\), so \(d_2=\vert5-(-5)\vert=\vert5 + 5\vert = 10\).

Step3: Calculate the total distance

The total distance \(D=d_1 + d_2\). Substitute \(d_1 = 5\) and \(d_2=10\) into the formula, we get \(D=5 + 10=15\).

Answer:

The distance from \((5,2)\) to \((5,-3)\) is \(5\) miles. The distance from \((5,-3)\) to \((-5,-3)\) is \(10\) miles. The total distance Ms. Dolphin drove is \(15\) miles.