Question

natasha walked from the library to the grocery store and then to her house. the diagram shows the top - view of the locations of these three places and their distances from each other. library 1.7 mi grocery store 0.9 mi natashas house which measurement is closest to the shortest distance in miles from natashas house to the library? a 2.6 mi b 2.3 mi c 1.4 mi d 1.8 mi

Explanation:

Step1: Identify right - triangle

The path from the library to the grocery store, the grocery store to the house, and the direct path from the house to the library form a right - triangle. The two legs of the right - triangle have lengths $a = 1.7$ mi and $b=0.9$ mi.

Step2: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is $c^{2}=a^{2}+b^{2}$, where $c$ is the length of the hypotenuse (the direct distance from the house to the library). So $c=\sqrt{a^{2}+b^{2}}=\sqrt{1.7^{2}+0.9^{2}}$.

Step3: Calculate values

First, calculate $1.7^{2}=2.89$ and $0.9^{2}=0.81$. Then $a^{2}+b^{2}=2.89 + 0.81=3.7$. So $c=\sqrt{3.7}\approx1.92$ mi.

Answer:

D. 1.9 mi