Question

The distance between the points (a cos θ, −a sin θ) and (a sin θ, a cos θ) is ______.

Options

• a

• `asqrt2`

• 0

• 2a

Answer 1

The distance between the points (a cos θ, −a sin θ) and (a sin θ, a cos θ) is `bbunderline(asqrt2)`.

Explanation:

d = `|sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)|`

= `|sqrt((a sin θ - a cos θ)^2 + (a cos θ + a sin θ)^2)|`

= `|sqrt(a^2 sin^2 θ + a^2 cos^2 θ - 2a^2  sin θ cos θ + a^2 cos^2 θ + a^2 sin^2 θ + 2a^2 sin θ cos θ)|`

= `|sqrt(2a^2 (sin^2 θ + cos^2 θ))|`

= `|sqrt(2a^2)|`

= `|sqrt(2a)|` units