Question

find the value of 'a' if the distance between the points A[ -3,-14] and B[a,-5] is 9 units please answer quickly i will mark it as brainlist

Answer 1

Answer:

-3

Step-by-step explanation:

Given points are A(-3,-14) and B(a,-5)

Here, x₁ = -3 , x₂ = a, y₁ = - 14, y₂ = -5.

Given that AB = 9 units.

Distance formula:

AB = √(x₂ - x₁)² + (y₂ - y₁)²

9 = √(a + 3)² + (-5 + 14)²

Squaring both sides, we get

81 = (a + 3)² + (-5 + 14)²

81 = a² + 9 + 6a + 81

a² + 6a + 9 = 0

a² + 3a + 3a + 9 = 0

a(a + 3) + a(a + 3) = 0

(a + 3)(a + 3) = 0

(a + 3)² = 0

a = -3.

Therefore, the value of a = -3.

Hope it helps!