To find out how much distance Keith would have saved by riding directly to the grocery store instead of taking the two legs of his journey, we can model his trip as a right triangle.
- The first leg of his trip is 2 miles.
- The second leg, after making a 90-degree turn, is also 2 miles.
Now, let's denote:
- one leg of the right triangle (first leg) as \( a = 2 \) miles,
- the other leg (second leg) as \( b = 2 \) miles.
Using the Pythagorean theorem, we can find the straight-line distance \( c \) (the hypotenuse) from his starting point to the grocery store:
\[ c = \sqrt{a^2 + b^2} \] \[ c = \sqrt{2^2 + 2^2} \] \[ c = \sqrt{4 + 4} \] \[ c = \sqrt{8} \] \[ c = 2\sqrt{2} \approx 2.828 \]
Next, let’s find the distance he traveled. The total distance Keith rode is: \[ 2 + 2 = 4 \text{ miles} \]
Now, we can determine how much distance he saved by riding directly to the store:
\[ \text{Distance saved} = \text{Distance traveled} - \text{Direct distance} \] \[ \text{Distance saved} = 4 - 2\sqrt{2} \approx 4 - 2.828 \approx 1.172 \]
Rounding this value to the nearest tenth:
\[ \text{Distance saved} \approx 1.2 \text{ miles} \]
Thus, the answer is:
1.2 miles