IF Q IS THE MIDLE POINT
asked Apr 1, 2013 in Geometry Answers by amitkr2693 (120 points)

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2 Answers

If Q is any point within a rectangle ABCD then QA^2+QC^2=QB^2+QD^2.by putting the value we get QD=squrt18.please comment if answer is right or not.
answered Jul 30, 2015 by partha Level 1 User (580 points)
Yes, your answer does appear to be correct, although it would have been helpful to show a bit more working, or quoting the theorem about the sum of the squares.
The person setting the question may not know the answer and may need help in finding out how to get it. The Best Answers are those with a good explanation as well as the right answer.
Here's my way of working it out:
Plot a rectangle A(0,0), B(0,a), C(b,a), D(b,0) where a and b are the lengths of the sides of a rectangle. Point Q(x,y) is anywhere in the rectangle.
AQ=sqrt(x^2+y^2); BQ=sqrt(x^2+(a-y)^2); CQ=sqrt((b-x)^2+(a-y)^2); DQ=sqrt((b-x)^2+y^2).
AQ^2+CQ^2=x^2+y^2 + (b-x)^2+(a-y)^2;
BQ^2+DQ^2=x^2+(a-y)^2 + (b-x)^2+y^2.
So for all points Q in a rectangle ABCD AQ^2+CQ^2=BQ^2+DQ^2, just as you stated! 9+25=16+QD^2 and QD=sqrt(34-16)=sqrt(18)=3sqrt(2).
QA2 + QC2 = QB2 + QD2,, 9 + 25 = 16 + QD2,, QD2 = 18 QD = √18 = 3√2 cm Ans
answered Aug 10 by Veer
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