Question

distance between two points ( 8 , -4 ) and ( 0 , a ) is 10. all the values are in the same unit of length. find the positive value of a

Answer 1

Feel free to ask if u don't understand something in the solution ..

Answer 2

The positive value of a = 2

Given :

The distance between two points (8 , - 4) and (0 , a) is 10. all the values are in the same unit of length

To find :

The positive value of a

Solution :

Step 1 of 2 :

Form the equation to find the value of a

Here it is given that distance between two points (8 , - 4) and (0 , a) is 10

Thus we get

$\displaystyle \sf{ \sqrt{ {(8 - 0)}^{2} + {( - 4 - a)}^{2} } = 10 }$

Step 2 of 2 :

Find the positive value of a

$\displaystyle \sf{ \sqrt{ {(8 - 0)}^{2} + {( - 4 - a)}^{2} } = 10 }$

$\displaystyle \sf{ \implies \sqrt{ {(8 )}^{2} + {( 4 + a)}^{2} } = 10}$

$\displaystyle \sf{ \implies {(8 )}^{2} + {( 4 + a)}^{2} = {10}^{2} }$

$\displaystyle \sf{ \implies 64 + {(a + 4)}^{2} = 100 }$

$\displaystyle \sf{ \implies {(a + 4)}^{2} = 100 - 64 }$

$\displaystyle \sf{ \implies {(a + 4)}^{2} = 36 }$

$\displaystyle \sf{ \implies a + 4 = \pm \: 6}$

Case : 1

a + 4 = 6 gives

a = 6 - 4

⇒ a = 2

Case : 2

a + 4 = - 6 gives

a = - 6 - 4

⇒ a = - 10

So the values of a are - 10 & 2

Hence the positive value of a = 2

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