Question

janet lives 8 kilometers due south of her parents house and 3 kilometers west of her grandparents house. on her birthday, janet drove from her house to her parents house. from there, she drove in a straight line to her grandparents house and then back home. how far did janet drive on her birthday? if necessary, round to the nearest tenth. kilometers

Explanation:

Step1: Calculate the distance from parents' house to grandparents' house

Use the Pythagorean theorem \(c = \sqrt{a^{2}+b^{2}}\), where \(a = 8\) (south - north distance) and \(b = 3\) (east - west distance).
\(c=\sqrt{8^{2}+3^{2}}=\sqrt{64 + 9}=\sqrt{73}\approx8.5\)

Step2: Calculate the total distance

The distance from Janet's house to parents' house is \(d_1=8\) km.
The distance from parents' house to grandparents' house is \(d_2\approx8.5\) km.
The distance from grandparents' house to Janet's house is \(d_3 = 3\) km (using the right - triangle sides, we can also verify by the fact that the path forms a triangle and we can use the sum of the sides).
The total distance \(D=d_1 + d_2+d_3\)
\(D=8+8.5 + 3=19.5\)

Answer:

\(19.5\)