Question

after school, carl and santo walk home. carl walks 10 blocks east and 9 blocks south. santo walks 9 blocks east and 2 blocks south. on the graph, the school is located at the origin. determine the distance between carls house (point c) and santos house (point s). enter the coordinates of the two given points and then calculate the distance between them. coordinates (x1, y1) of point c: (?,?) coordinates (x2, y2) of point s: (?,?) d = \sqrt{(x2 - x1)^2+(y2 - y1)^2}

Explanation:

Step1: Determine Carl's coordinates

Since Carl walks 10 blocks east (positive x - direction) and 9 blocks south (negative y - direction) from the origin (0, 0), the coordinates of point C are $(10,-9)$.

Step2: Determine Santo's coordinates

Since Santo walks 9 blocks east (positive x - direction) and 2 blocks south (negative y - direction) from the origin (0, 0), the coordinates of point S are $(9,-2)$.

Step3: Calculate the distance

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 10,y_1=-9,x_2 = 9,y_2=-2$.
$d=\sqrt{(9 - 10)^2+(-2+9)^2}=\sqrt{(-1)^2 + 7^2}=\sqrt{1 + 49}=\sqrt{50}=5\sqrt{2}\approx7.07$

Answer:

Coordinates $(x_1,y_1)$ of point C: $(10,-9)$
Coordinates $(x_2,y_2)$ of point S: $(9,-2)$
Distance $d\approx7.07$