Question

Steve draws a line from (-2, -6) to (3, 9). Approximately how long is the line he draws?

Answer 1

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Let : A = ( - 2 , - 6 ) & B = ( 3 , 9 )

`d = distance \: \: between \: \: points \\`

`d = \sqrt{ ( \: {y(B) - y(A) } \: )^(2) + ( \: { x(B) - x(A) } \: )^(2) } \\`

`d = \sqrt{ ( \: {9 - ( - 6)} \: )^(2) + ( \: {3 - ( - 2)} \: )^(2) } \\`

`d = \sqrt{ ( \: {9 + 6} \: )^(2) + ( \: {3 + 2} \: )^(2) } \\`

`d = \sqrt{ {15}^(2) + {5}^(2) }`

`d = √(225 + 25)`

`d = √(250)`

`d = √(25 * 10)`

`d = \sqrt{ {5}^(2) * 10 }`

`d = 5 √(10)`

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Thus Steve draws a line which has a length of 5√10 .

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