Question

places in joes town
what is the shortest distance, in miles, between the school and the library? round your answer to the nearest tenth.
□ miles.

Explanation:

Step1: Identify coordinates

Library: \((-3, 4)\) (assuming each grid unit is 1, since Library is at x=-3 (between -4 and -2, mid? Wait, looking at the grid: x-axis: -6, -4, -2, 0, 2, 4, 6. Library is at x=-3? Wait, no, the Library is at x=-3? Wait, the x-coordinate: the Library is at column -3? Wait, the grid lines: the Library is at x=-3? Wait, no, let's check the positions. Home is at (2, 3)? Wait, no, the y-axis: 6,4,2,0,-2,-4,-6. Library: y=4, x: between -4 and -2? Wait, the Library is at x=-3? Wait, no, the School is at (4, 2), Home at (2, 3), Library at (-3, 4)? Wait, no, let's count the grid. Each square is 1 unit. So Library: x=-3? Wait, the x-axis: from -6 to 6, with ticks at -6, -4, -2, 0, 2, 4, 6. So between -4 and -2 is -3. So Library is at (-3, 4). School is at (4, 2).

Step2: Apply distance formula

Distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
\(x_1 = -3\), \(y_1 = 4\); \(x_2 = 4\), \(y_2 = 2\)
\(d = \sqrt{(4 - (-3))^2 + (2 - 4)^2}\)
\(= \sqrt{(7)^2 + (-2)^2}\)
\(= \sqrt{49 + 4}\)
\(= \sqrt{53}\)
\(\approx 7.3\) (since \(\sqrt{53} \approx 7.28\), rounded to nearest tenth is 7.3)

Answer:

7.3