Question

Find the distances between the following point.

R(–3a, a), S(a, –2a)

Answer 1

R(–3a, a), S(a, –2a)

Let R (x₁, y₁) and S (x₂, y₂) be the given points.

∴ x₁ = –3a, y₁ = a, x₂ = a, y₂ = –2a

By distance formula,

 d(R, S) = \[\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\]

= \[\sqrt{\left[\mathrm{a-(-3a)}\right]^{2}+\left(-2\mathrm{a-a}\right)^{2}}\]

= \[\sqrt{\left(\mathrm{a + 3a}\right)^{2}+\left(-2\mathrm{a-a}\right)^{2}}\]

= \[\sqrt{\left(\mathrm{4a}\right)^{2}+\left(\mathrm{-3a}\right)^{2}}\]

= \[\sqrt{16\mathbf{a}^{2}+9\mathbf{a}^{2}}\]

= \[\sqrt{25\mathbf{a}^{2}}\]

= 5a

∴ d(R, S) = 5a units