★CHALLENGE★
Prove the following statement by contradictory method
"There is no point on x axis that is equidistant from P(3, 2) and P(3, -1)"
Answers
Given Nothing, ha!
To prove :
"There is no point on x axis that is equidistant from P(3, 2) and P(3, -1)"
Ok, here is your proof....
Proof:
Let us now assume that there is a point on x axis that is equidistant from P(3, 2) and Q(3, -1)
So here we need to let the point that is equidistant from P & Q.
Let the required point R(x, 0)
now, ATC (according to condition)
So, by distance formula
Distance b|w P & R = Distance b|w Q & R
=> √{(3 - x)² + (2 - 0)²} = √{(3 - x)² + (0 - 1)²}
(Squaring both sides we get)
=> (3 - x)² + (2 - 0)² = (3 - x)² + (0 - 1)²
=> (3 - x)² + ( 2 )² = (3 - x)² + ( -1)²
Eliminating (3 - x)² from both sides we get
=> 2² = 1²
=> 4 = 1
Here... we get a false statement, 4 = 1
But in actual 4 ≠ 1
Such contradiction of this fact occurred due to assuming a point i.e equidistant from P(3, 2) & Q(3, -1)
Thus, we must say that there is no point on x axis that would be equidistant from P & Q.
Hence proved.