Question

If the distance between the points (3, a)and (6, 1) is 5, then find the value of a.
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Answer 1

Answer:

Points can be (-3) or 5 .

Step-by-step explanation:

Given points are ,

• (3,a)
• (6,1)

And , the distance between them is 5 .

So , we know the Distance Formula as ,

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=> Distance = √[ (x2 - x1)² + (y2 -y1)²

=> Distance = √ [ ( 3 - 6 )² + ( a - 1 ) ² ]

=> 5 = √ [ (-3)² + a² + 1 - 2a ]

=> 25 = 9 + a² + 1 - 2a

=> 25 - 10 = a² - 2a

=> a² - 2a = 15

=> a² - 2a - 15 = 0

=> a² - 5a + 3a - 15 = 0

=> a ( a - 5 ) + 3 ( a - 5 ) = 0

=> ( a - 5 ) ( a + 3 ) = 0

=> a = 5 , (-3)