Question

Find the distance between the points:

P(a + b, a – b) and Q(a – b, a + b)

Answer 1

P(a + b, a - b) and Q(a - b, a + b)

The given points are P(a + b, a - b) and Q(a - b, a + b)

Then (x₁ = a + b, y₁ = a - b) and (x₂ = a - b, y₂ = a + b)

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

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

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

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

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

= `sqrt(8b^2)`

= `sqrt(4 xx2b^2)`

= `2 sqrt(2b)` units