Question

The distance on a city grid is measured in blocks. On the grid, the coordinates for the location of your house are (2,6). The Internet Cafe is located at (12, 8), and your friend lives at point (8,4). If you leave your house, visit the Internet Cafe, and then go to your friend's house, how far have you traveled? Round your answer to the nearest whole block. A) 10 blocks
B) 14 blocks
C) 16 blocks
D) 18 blocks
E) 20 blocks

Answer 1

The answer is C) 16 blocks.

We will use the distance formula for this problem:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

From your house to the internet cafe:

$d=\sqrt{(8-6)^2+(12-2)^2}=\sqrt{2^2+10^2}=\sqrt{4+100} \\ \\=\sqrt{104}=10.2$

From the internet cafe to your friend's house:
$d=\sqrt{(8-4)^2+(12-8)^2}=\sqrt{4^2+4^2}=\sqrt{16+16}=\sqrt{32}=5.7$

Together, we have 10.2+5.7=15.9, which rounds to 16 blocks.