Jayden lives 7.7 kilometers due south of his parents' house and 2.7 kilometers west of his grandparents' house. On his birthday, Jayden drove from his house to his parents' house.... Jayden lives 7.7 kilometers due south of his parents' house and 2.7 kilometers west of his grandparents' house. On his birthday, Jayden drove from his house to his parents' house. From there, he drove in a straight line to his grandparents' house and then back home. How far did Jayden drive on his birthday? If necessary, round to the nearest tenth. Read more

Steps to Solve

1. Calculate the distance from Jayden’s house to his parents' house
   Jayden lives 7.7 kilometers south of his parents' house. So, the distance he drives to his parents' house is:
   Distance to parents = $7.7$ km

2. Identify the position of his grandparents' house
   His grandparents' house is located 2.7 kilometers west of his grandparents' house. Since the parents' house is east of the location, we need to plot the two points:

• Parents' house: $(0, 0)$
• Jayden’s house: $(0, -7.7)$
• Grandparents' house: $(-2.7, 0)$

3. Calculate the distance from the parents' house to the grandparents' house
   Use the distance formula:
   $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$
   Plugging in the coordinates of the two houses:
   $$ d = \sqrt{(-2.7 - 0)^2 + (0 - 0)^2} $$
   $$ d = \sqrt{(-2.7)^2 + 0} = \sqrt{7.29} \approx 2.7 \text{ km} $$

4. Calculate the total distance driven
   Jayden drives to his parents' house, then to his grandparents', and back to his house:
   Total distance = Distance to parents + Distance to grandparents + Distance back to parents
   Total distance = $7.7 + 2.7 + 2.7$
   Total distance = $13.1$ km