Question

Find the distance between the points

P(a + b,a - b)andQ(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)andQ(a -b,a + b)

`Then (x_1 = a +b, y_1= a-b) and (x_2 = a-b, y_2 = 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