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Question
Find the distance between the points
P(a + b,a - b)andQ(a -b,a + b)
Solution
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
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