Question

Jack started from his home (2, 2) and moved 6 units on the positive x-axis and 10 units on the positive y-axis to reach his office. Find the distance between Jack's home and office in miles. (Take √34 = 5.8)

• A. 12.6 units
• B. 11 units
• C. 11.6 units
• D. 16 units

Answer 1

The correct option is C 11.6 units

Let the coordinates of home be "H" and the coordinates of office be "O".
Jack started from his home H(2,2).

Jack has moved 6 units in the positive x-axis direction to reach the office.
∴ x-coordinate of O = 2 + 6 = 8

Jack has moved 10 units in the positive y-axis direction to reach office.
∴ y-coordinate of O = 2 + 10 = 12

So, the coordinates of O are (8, 12).

We know that, the distance between the points $(x_1,y_1)$ and $(x_2,y_2)$ is represented as:

$\text{Distance, d}=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

So, the distance "d" between H(2,2) and O(8,12) is:

$\text{d}=\sqrt{(8-2{)}^2+(12-2{)}^2}$

$\Rightarrow \text{d}=\sqrt{6^2+{10}^2}$

$\Rightarrow \text{d}=\sqrt{36+100}$

$\Rightarrow \text{d}=\sqrt{136}$

$\Rightarrow \text{d}=2\sqrt{34}$

$\Rightarrow \text{d}=2\times 5.8$

$\Rightarrow \text{d}=11.6$

So, the distance between Jack's home and office is 11.6 units.