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. elliot? (round to the nearest tenth)

Explanation:

Step1: Determine the coordinate - like positions

Let the school (CTK) be the origin \((0,0)\). Mr. Laughlin's position is \((- 8,6)\) (west is negative in the x - direction and north is positive in the y - direction), and Mr. Elliott's position is \((30,-16)\) (east is positive in the x - direction and south is negative in the 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 \(y_2 - y_1\): \(x_2 - x_1=30-(-8)=38\), \(y_2 - y_1=-16 - 6=-22\). Then, \(d=\sqrt{(38)^2+(-22)^2}=\sqrt{1444 + 484}=\sqrt{1928}\).

Step3: Calculate the square - root and round

\(\sqrt{1928}\approx43.9\).

Answer:

43.9