Question

An airplane is moving in the sky from one position to another position. It moved 6 units towards the west and 8 units towards the north. The distance between the starting and final positions is 10 units. Which of the following points indicate the above path covered by the airplane?

• A. (0,0), (0,6), and (6,6)
• B. (0,0), (7,7), and (7,8)
• C. (0,0), (6,0), and (8,8)
• D. (0,0), (6,0), and (6,8)

Answer 1

The correct option is D (0,0), (6,0), and (6,8)

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

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

Option 'a':
Let's check the first option A(0,0), B(6,0), and C(6,8)

The distance between the points (0,0) and (6,0) is

$\Rightarrow \sqrt{(6-0{)}^2+(0-0{)}^2}$

$\Rightarrow \sqrt{(6{)}^2+(0{)}^2}$

$\Rightarrow \sqrt{36+0}$

$\Rightarrow \sqrt{36}$

$\Rightarrow 6$ units


The distance between the points (6,0) and (6,8) is

$\Rightarrow \sqrt{(6-6{)}^2+(8-0{)}^2}$

$\Rightarrow \sqrt{(0{)}^2+(8{)}^2}$

$\Rightarrow \sqrt{0+64}$

$\Rightarrow \sqrt{64}$

$\Rightarrow 8$ units


The distance between the points (0,0) and (6,8) is

$\Rightarrow \sqrt{(6-0{)}^2+(8-0{)}^2}$

$\Rightarrow \sqrt{(6{)}^2+(8{)}^2}$

$\Rightarrow \sqrt{36+64}$

$\Rightarrow \sqrt{100}$

$\Rightarrow 10$ units

The distance of 10 units matches with the given information. So, option 'a' is correct.


Option 'b':
Let's check the first option A(0,0), B(0,6), and C(6,6)

The distance between the points (0,0) and (0,6) is

$\Rightarrow \sqrt{(0-0{)}^2+(6-0{)}^2}$

$\Rightarrow \sqrt{(0{)}^2+(6{)}^2}$

$\Rightarrow \sqrt{0+36}$

$\Rightarrow \sqrt{36}$

$\Rightarrow 6$ units

The distance between the points (0,6) and (6,6) is

$\Rightarrow \sqrt{(6-0{)}^2+(6-6{)}^2}$

$\Rightarrow \sqrt{(6{)}^2+(0{)}^2}$

$\Rightarrow \sqrt{36+0}$

$\Rightarrow \sqrt{36}$

$\Rightarrow 6$ units


The distance between the points (0,0) and (6,6) is

$\Rightarrow \sqrt{(6-0{)}^2+(6-0{)}^2}$

$\Rightarrow \sqrt{(6{)}^2+(6{)}^2}$

$\Rightarrow \sqrt{36+36}$

$\Rightarrow \sqrt{72}$

The distance of √72 units does not match with the given information. So, option 'b' is incorrect.


Option 'c':
Let's check the first option A(0,0), B(6,0), and C(8,8)

The distance between the points (0,0) and (6,0) is

$\Rightarrow \sqrt{(6-0{)}^2+(0-0{)}^2}$

$\Rightarrow \sqrt{(6{)}^2+(0{)}^2}$

$\Rightarrow \sqrt{36+0}$

$\Rightarrow \sqrt{36}$

$\Rightarrow 6$ units

The distance between the points (6,0) and (8,8) is

$\Rightarrow \sqrt{(8-6{)}^2+(8-0{)}^2}$

$\Rightarrow \sqrt{(2{)}^2+(8{)}^2}$

$\Rightarrow \sqrt{4+64}$

$\Rightarrow \sqrt{68}$

The distance between the points (0,0) and (8,8) is

$\Rightarrow \sqrt{(8-0{)}^2+(8-0{)}^2}$

$\Rightarrow \sqrt{(8{)}^2+(8{)}^2}$

$\Rightarrow \sqrt{64+64}$

$\Rightarrow \sqrt{128}$

The distance of √128 units does not match with the given information. So, option 'c' is incorrect.


Option 'd':
Let's check the fourth option A(0,0), B(7,7), and C(7,8)

The distance between the points (0,0) and (7,7) is

$\Rightarrow \sqrt{(7-0{)}^2+(7-0{)}^2}$

$\Rightarrow \sqrt{(7{)}^2+(7{)}^2}$

$\Rightarrow \sqrt{49+49}$

$\Rightarrow \sqrt{98}$

The distance between the points (0,0) and (7,8) is

$\Rightarrow \sqrt{(7-0{)}^2+(8-0{)}^2}$

$\Rightarrow \sqrt{(7{)}^2+(8{)}^2}$

$\Rightarrow \sqrt{49+64}$

$\Rightarrow \sqrt{113}$

The distance between the points (7,7) and (7,8) is

$\Rightarrow \sqrt{(7-7{)}^2+(7-8{)}^2}$

$\Rightarrow \sqrt{(0{)}^2+(1{)}^2}$

$\Rightarrow \sqrt{0+1}$

$\Rightarrow \sqrt{1}$

$\Rightarrow 1$

The distance of 1 unit does not match with the given information. So,
option 'd' is incorrect.