Question

ex. 4) suppose that mr. laughlin lives 8 blocks west and 6 blocks north of ctk, while mr. elliott lives 30 blocks east and 16 blocks south of the school. how far apart does mr. laughlin and mr. elliott live?
a. draw a picture:
b. approximately how many blocks separate mr. laughlin and mr. elliott? (round to the nearest tenth)
ex. 5) suppose that mr. bajner lives 9 blocks west and 40 blocks south of ctk, while mr. zundel lives 20 blocks north and 21 blocks east of the school. how far apart does mr. bajner and mr. zundel live?
c. draw a picture:

Explanation:

Step1: Determine the coordinate - like positions

Let the school be the origin \((0,0)\). Mr. Laughlin's position is \((- 8,6)\) (west is negative x - direction and north is positive y - direction) and Mr. Elliott's position is \((30,-16)\) (east is positive x - direction and south is negative y - direction).

Step2: Use the distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-8,y_1 = 6,x_2 = 30,y_2=-16\). First, find \(x_2 - x_1\) and \(y_2 - y_1\): \(x_2 - x_1=30-(-8)=38\) and \(y_2 - y_1=-16 - 6=-22\).

Step3: Calculate the distance

Then \(d=\sqrt{38^2+(-22)^2}=\sqrt{1444 + 484}=\sqrt{1928}\approx43.9\).

Answer:

43.9