Question

after school, andrew and ellen walk home. andrew walks 2 blocks west and 6 blocks north. ellen walks 13 blocks west and 2 blocks north. on the graph, the school is located at the origin. determine the distance between andrews house (point a) and ellens house (point e). enter the coordinates of the two given points and then calculate the distance between them. coordinates (x1, y1) of point a: (?,?) coordinates (x2, y2) of point e: (?,?) d = \sqrt{(x2 - x1)^2+(y2 - y1)^2} d = \sqrt{( )^2+( )^2}

Explanation:

Step1: Determine coordinates of point A

Andrew walks 2 blocks west (negative x - direction) and 6 blocks north (positive y - direction) from the origin (0, 0). So the coordinates of point A are $(- 2,6)$.

Step2: Determine coordinates of point E

Ellen walks 13 blocks west (negative x - direction) and 2 blocks north (positive y - direction) from the origin (0, 0). So the coordinates of point E are $(-13,2)$.

Step3: Calculate distance between A and E

Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-2,y_1 = 6,x_2=-13,y_2 = 2$.
$d=\sqrt{(-13-(-2))^2+(2 - 6)^2}=\sqrt{(-13 + 2)^2+(-4)^2}=\sqrt{(-11)^2+(-4)^2}=\sqrt{121 + 16}=\sqrt{137}$.

Answer:

The coordinates of point A are $(-2,6)$, the coordinates of point E are $(-13,2)$ and the distance $d=\sqrt{137}$.