Question

5. If the distance between the points (3, a) and(4,1) is √10, then the

value of a is_​

Answer 1

Answer:

a = -2 or a = 4

Step-by-step explanation:

Let the points be A and B

we know that,

coordinates of A - (3,a)

coordinates of B - (4,1)

Given that,

AB = √10 units

∴ using distance formula,

AB = √(4 - 3)² + (1 - a)²

⇒ √10 = √(1)² + (1 + a² - 2a)

squaring on both sides,

10 = 1 + 1 + a² - 2a

⇒ a² - 2a - 8 = 0

⇒a² - 4a + 2a - 8 = 0

⇒a(a - 4) + 2(a - 4) = 0

⇒(a+2) (a-4) = 0

∴ a = -2 or a = 4

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Answer 2

Answer:

let we take point p and q

p(3,a) , q(4,1)

Step-by-step explanation:

distance b/w p and q = √10

√(4-3)²+(1-a)² = √10

√(1)²+(1-a)² = √10

squaring both sides

1+ (1-a)² = 10

1  + a² - 2a = 9

a² - 2a = 8

a²- 2a - 8 = 0

after solving quadratic equation by quadratic formula or middle term splitting we get a = 4 and -2