Question

after school, felix and rahul walk home. felix walks 3 blocks west and 12 blocks north. rahul walks 12 blocks east and 4 blocks north. on the graph, the school is located at the origin. determine the distance between felixs house (point f) and rahuls house (point r). enter the coordinates of the two given points and then calculate the distance between them. coordinates (x1, y1) of point f: (?,?) coordinates (x2, y2) of point r: (?,?) d = \sqrt{(x2 - x1)^2+(y2 - y1)^2} d = \sqrt{( )^2+( )^2} d =

Explanation:

Step1: Determine Felix's coordinates

West is negative x - direction and north is positive y - direction. Felix walks 3 blocks west and 12 blocks north from the origin (0, 0). So the coordinates of point F are $(-3,12)$.

Step2: Determine Rahul's coordinates

East is positive x - direction and north is positive y - direction. Rahul walks 12 blocks east and 4 blocks north from the origin. So the coordinates of point R are $(12,4)$.

Step3: Substitute into distance formula

The distance formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-3,y_1 = 12,x_2=12,y_2 = 4$. Then $d=\sqrt{(12-(-3))^2+(4 - 12)^2}=\sqrt{(12 + 3)^2+(-8)^2}=\sqrt{15^2+(-8)^2}=\sqrt{225 + 64}=\sqrt{289}$.

Step4: Calculate the distance

$\sqrt{289}=17$.

Answer:

Coordinates $(x_1,y_1)$ of point F: $(-3,12)$
Coordinates $(x_2,y_2)$ of point R: $(12,4)$
$d=\sqrt{(12-(-3))^2+(4 - 12)^2}$
$d=\sqrt{(15)^2+(-8)^2}$
$d = 17$