SOLUTION: I don't have the slightest clue on how to solve this. Please help, it says to use coordinate geometry to prove that the diagonals of a rectangle are congruent, where: p(0,b) and Q(

Algebra ->  Rectangles -> SOLUTION: I don't have the slightest clue on how to solve this. Please help, it says to use coordinate geometry to prove that the diagonals of a rectangle are congruent, where: p(0,b) and Q(      Log On


   

Question 136809This question is from textbook algebra
: I don't have the slightest clue on how to solve this. Please help, it says to use coordinate geometry to prove that the diagonals of a rectangle are congruent, where: p(0,b) and Q(a,b) which lie on the vertical y. And O(0,0) and R(a,0) which lie on the horizantel line x.
Please help me, it's ver confusing to me. Thank You=) This question is from textbook algebra

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Your task is to prove that the measure of OQ is equal to the measure of PR.

Use the distance formula:

d%5BPR%5D=sqrt%28%28x%5BP%5D-x%5BR%5D%29%5E2%2B%28y%5BP%5D-y%5BR%5D%29%5E2%29%29
d%5BPR%5D=sqrt%28%280-a%29%5E2%2B%28b-0%29%5E2%29%29
d%5BPR%5D=sqrt%28a%5E2%2Bb%5E2%29%29

So, now we have an expression in simplest terms for the length of the segment PR.

Do the same thing with the coordinate values for the points O and Q to develop an expression for the length of segment OQ. If the expressions are equal or equivalent, then the segments are congruent, otherwise not.