Question

to get to his parents house, tyler would have to drive due north 6 kilometers. to get to his grandparents house, he would have to drive due east 6 kilometers. what is the straight-line distance between the parents and grandparents houses? if necessary, round to the nearest tenth.
\boxed{} kilometers

Explanation:

Step1: Identify the triangle type

The paths to parents' (north) and grandparents' (east) houses form a right - triangle, with legs \(a = 6\) km and \(b = 6\) km, and the straight - line distance is the hypotenuse \(c\).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle, \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 6\) and \(b = 6\) into the formula:
\[

$$\begin{align*} c&=\sqrt{6^{2}+6^{2}}\\ &=\sqrt{36 + 36}\\ &=\sqrt{72}\\ &=\sqrt{36\times2}\\ &=6\sqrt{2}\\ &\approx6\times1.414\\ &\approx8.5 \end{align*}$$

\]

Answer:

\(8.5\)