Question

The diagram shows the locations of three towns and a library. Each unit on the grid represents 1.5 kilometers.
a. The actual distance between the library and Town A is_km.

b. The approximate distance between the library and Town B is_km.

c. Amelia traveled from Town A to the library to return her books. She then traveled to Town B to meet her friend. She and her friend then traveled to Town C and had dinner. How far did Amelia travel?

Answer 1

Answer:

a. 6km

b. 6.185 km

c. 18.37 km

Step-by-step explanation:

The question is on finding the distance of between two points

The general formulae is given by;

$d= \sqrt{(X2-X1)^2+(Y2-Y1)^2}$

Where d is the distance

Given that;

1 unit on grid = 1.5 km

a. Finding distance between the library and Town A

A (-2,3)  and library (2,3)

$d= \sqrt{(2- -2)^2  + (3-3)^2} \\\\= \sqrt{4^2} \\= 4$

Actual distance = 4 × 1.5 = 6 km

b. Distance between the library and Town B is

library (2,3)  and town B (1, -1)

$d=\sqrt{(1-2)^2+ (-1-3)^2} \\\\\\d=\sqrt{-1^2 +-4^2}\\ \\\\d=\sqrt{1+16} \\\\\\d=\sqrt{17}  = 4.123$

Actual distance = 4.123×1.5 =6.185 km

c. First find the distance between Town B and Town C

Town B (1, -1) and Town C (-3,-2)

$d=\sqrt{(-3-1)^2 + (-2--1)^2} \\\\d=\sqrt{-4^2 + -1^2} \\\\d=\sqrt{16+1} \\\\d=\sqrt{17} \\\\d=4.123$

Actual distance= 4.123×1.5 =6.185 km

Total distance traveled by Amelia = 6 +6.185 +6.185 =18.37 km