Question

Find the distance between the points (a, b) and (−a, −b).

Answer 1

Using distance formula:
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2 )`

Here, x₁ = a, y₁ = b, x₂ = - a and y₂ = - b
On substituting the values in the formula we get

= `sqrt(( - a - a)^2 + ( - b - b)^2)`

= `sqrt((- 2a)^2 + (-2b)^2)`

= `sqrt( 4a^2 + 4b^2)`

= `2sqrt(a^2 + b^2 )`
Therefore, the distance between (a, b) and (−a,−b) is `2sqrt(a^2 + b^2 )`.