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

a. 6km

b. 6.185 km

c. 18.37 km

Explanation:

The question is on finding the distance of between two points

The general formulae is given by;

`d= √((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= √((2- -2)^2  + (3-3)^2) \\\\= √(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=√((1-2)^2+ (-1-3)^2) \\\\\\d=√(-1^2 +-4^2)\\ \\\\d=√(1+16) \\\\\\d=√(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=√((-3-1)^2 + (-2--1)^2) \\\\d=√(-4^2 + -1^2) \\\\d=√(16+1) \\\\d=√(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