Question

Jack started from the home (1, 1) and moved 8 units on the x-axis and 6 units on the y-axis to reach his office. Find the distance between home and office.
units

Answer 1

Let the coordinates of home be "H" and the coordinates of office be "O"
Jack started from the home H(1, 1).

Given Data:

• Jack has moved 8 units in the x-axis direction to reach office ∴ x-coordinates of O = 1 + 8 = 9
• Jack has moved 6 units in the y-axis direction to reach office ∴ y-coordinates of O = 1 + 6 =7

So, the coordinates of O are (9, 7).

We know that, the distance between the points $(x_1,y_1)$ and $(x_2,y_2)$
$=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\therefore$ The distance between H(1, 1) and O(9, 7)
$=\sqrt{(9-1{)}^2+(7-1{)}^2}$
$=\sqrt{8^2+6^2}$
$=\sqrt{64+36}$
$=\sqrt{100}$
$=10$

Hence, the distance between home and office is 10 units.