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Question
Find the distance between the points:
P(a + b, a - b) and Q(a - b, a + b)
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Solution
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
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