Question

Find the value of a, if the distance between the points A (-3,-14) and P (a,-5) is 9 units .

Answer 1

Given,

• A = (-3 , -14) = (a₁ , a₂)
• B = (a , -5)  = (b₁ , b₂)
• Distance between A and B (D) = 9 units

Here, we have to use the distance formula ,

$\boxed{\bold{D=\sqrt{(a_1-b_1)^2+(a_2-b_2)^2}}}}$

Applying the values to the equation,

$\bold{\sqrt{(-3-a)^2+(-14+5)^2}=9}$

$\implies{\bold{\sqrt{(-3-a)^2+(-9)^2}=9}}$

Squaring  both the sides,

$\implies{\bold{(-3-a)^2+(-9)^2= 9^2}$

$\implies{\bold{(-3-a)^2+81=81}}$

$\implies{\bold{(-3-a)^2=0}}$

$\implies{\bold{-3-a=0}}$

$\boxed{\implies{\bold{a=-3}}}$