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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?

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

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