Question

after school, marcos and henry walk home. marcos walks 5 blocks west and 8 blocks north. henry walks 12 blocks west and 4 blocks north. on the graph, the school is located at the origin. determine the distance between marcos house (point m) and henrys house (point h). enter the coordinates of the two given points and then calculate the distance between them. coordinates $(x_1,y_1)$ of point m: coordinates $(x_2,y_2)$ of point h: $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Explanation:

Step1: Determine coordinates of point M

Since west is negative x - direction and north is positive y - direction, for Marcos who walks 5 blocks west and 8 blocks north from the origin (0,0), the coordinates of point M are $(- 5,8)$.

Step2: Determine coordinates of point H

Henry walks 12 blocks west and 4 blocks north from the origin. So the coordinates of point H are $(-12,4)$.

Step3: Apply distance formula

The distance formula is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-5,y_1 = 8,x_2=-12,y_2 = 4$.
Substitute the values:

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Answer:

The coordinates of point M are $(-5,8)$, the coordinates of point H are $(-12,4)$, and the distance between them is $\sqrt{65}$ blocks.