Question

If the distance between the points (a,2a) and (4a,6a) is 20 units. Find the value of a.

Answer 1

      $\underline{\bold{Answer:}}$

      $+4,-4$

      $\underline{\bold{Step-by-step-explaination:}}$

      $\text{The two given points are }(a,2a) \text{ and }(4a,6a), \text{the distance between them}\\\text{is }20 \text{ units}$

      $\text{Applying the distance formula}$

$\implies \boxed{\sqrt{(a-4a)^{2} + (2a-6a)^{2}}= 20}$

$\implies \boxed{\sqrt{(-3a)^{2} + (-4a)^{2} } = 20}$

$\implies \boxed{\sqrt{(9a^{2} + 16a^{2}}=20}$

$\implies \boxed{\sqrt{25a^{2} }} = 20$

      $\text{Squaring both sides}$

$\implies \boxed{25a^{2} = (20)^{2} }$

$\implies \boxed{25a^{2} = 400}$

$\implies \boxed{a^{2}= 16}$

$\implies \boxed{a = \sqrt{16}}$

      $\text{We know that }\sqrt{x^{2}} = +x,-x$

$\implies \boxed{a = +4,-4}$