Question

★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)"

​

Answer 1

Step-by-step explanation:

Given : (・–・;)ゞ 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)

(~_~メ)

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....

And it was how I completed my challenge....