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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?

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Solution

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

We know that, the distance between the points (x1,y1) and (x2,y2) is represented as:

Distance, d=√(x2−x1)2+(y2−y1)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

⇒√(6−0)2+(0−0)2

⇒√(6)2+(0)2

⇒√36+0

⇒√36

⇒6 units

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

⇒√(6−6)2+(8−0)2

⇒√(0)2+(8)2

⇒√0+64

⇒√64

⇒8 units

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

⇒√(6−0)2+(8−0)2

⇒√(6)2+(8)2

⇒√36+64

⇒√100

⇒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

⇒√(0−0)2+(6−0)2

⇒√(0)2+(6)2

⇒√0+36

⇒√36

⇒6 units

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

⇒√(6−0)2+(6−6)2

⇒√(6)2+(0)2

⇒√36+0

⇒√36

⇒6 units

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

⇒√(6−0)2+(6−0)2

⇒√(6)2+(6)2

⇒√36+36

⇒√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

⇒√(6−0)2+(0−0)2

⇒√(6)2+(0)2

⇒√36+0

⇒√36

⇒6 units

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

⇒√(8−6)2+(8−0)2

⇒√(2)2+(8)2

⇒√4+64

⇒√68

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

⇒√(8−0)2+(8−0)2

⇒√(8)2+(8)2

⇒√64+64

⇒√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

⇒√(7−0)2+(7−0)2

⇒√(7)2+(7)2

⇒√49+49

⇒√98

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

⇒√(7−0)2+(8−0)2

⇒√(7)2+(8)2

⇒√49+64

⇒√113

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

⇒√(7−7)2+(7−8)2

⇒√(0)2+(1)2

⇒√0+1

⇒√1

⇒1

The distance of 1 unit does not match with the given information. So,

__option 'd'__ is incorrect.

We know that, the distance between the points (x1,y1) and (x2,y2) is represented as:

Distance, d=√(x2−x1)2+(y2−y1)2

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

⇒√(6−0)2+(0−0)2

⇒√(6)2+(0)2

⇒√36+0

⇒√36

⇒6 units

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

⇒√(6−6)2+(8−0)2

⇒√(0)2+(8)2

⇒√0+64

⇒√64

⇒8 units

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

⇒√(6−0)2+(8−0)2

⇒√(6)2+(8)2

⇒√36+64

⇒√100

⇒10 units

The distance of 10 units matches with the given information. So,

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

⇒√(0−0)2+(6−0)2

⇒√(0)2+(6)2

⇒√0+36

⇒√36

⇒6 units

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

⇒√(6−0)2+(6−6)2

⇒√(6)2+(0)2

⇒√36+0

⇒√36

⇒6 units

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

⇒√(6−0)2+(6−0)2

⇒√(6)2+(6)2

⇒√36+36

⇒√72

The distance of

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

⇒√(6−0)2+(0−0)2

⇒√(6)2+(0)2

⇒√36+0

⇒√36

⇒6 units

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

⇒√(8−6)2+(8−0)2

⇒√(2)2+(8)2

⇒√4+64

⇒√68

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

⇒√(8−0)2+(8−0)2

⇒√(8)2+(8)2

⇒√64+64

⇒√128

The distance of

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

⇒√(7−0)2+(7−0)2

⇒√(7)2+(7)2

⇒√49+49

⇒√98

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

⇒√(7−0)2+(8−0)2

⇒√(7)2+(8)2

⇒√49+64

⇒√113

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

⇒√(7−7)2+(7−8)2

⇒√(0)2+(1)2

⇒√0+1

⇒√1

⇒1

The distance of 1 unit does not match with the given information. So,

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