Question

after school, harvey and kordell walk home. harvey walks 4 blocks west and 10 blocks south. kordell walks 12 blocks west and 1 block south. on the graph, the school is located at the origin. determine the distance between harveys house (point h) and kordells house (point k). enter the coordinates of the two given points and then calculate the distance between them. coordinates (x1, y1) of point h: (?,?) coordinates (x2, y2) of point k: (?,?) d = \sqrt{(x2 - x1)^2+(y2 - y1)^2}

Explanation:

Step1: Determine H's coordinates

West is negative x - direction, south is negative y - direction. So H: $(-4,-10)$.

Step2: Determine K's coordinates

K walks 12 blocks west and 1 block south, so K: $(-12,-1)$.

Step3: Calculate the distance

Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-4,y_1 = - 10,x_2=-12,y_2=-1$.
$d=\sqrt{(-12-(-4))^2+((-1)-(-10))^2}=\sqrt{(-8)^2 + 9^2}=\sqrt{64 + 81}=\sqrt{145}\approx12.04$

Answer:

Coordinates of point H: $(-4,-10)$
Coordinates of point K: $(-12,-1)$
Distance $d\approx12.04$