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Question

A(3, 0) is the midpoint of the line joining P(3, 3) and Q(3, -3).


  1. True

  2. False


Solution

The correct option is A

True


If the point (3,0) is the midpoint of the line joining (3,3) and (3,-3), then, it is equidistant from both the points.
AP=(33)2+(30)2=3 (1)AQ=(33)2+(3(0))2=3 (2)

From (1) and (2),
AP=AQ.
The line joining P and Q is x=3. This is because the x coordinates of P and Q are equal to 3. So, the points P and Q lie on the line in which any point has its x coordinate equal to 3. Point A also lies on the same line x=3.

Since point A lies on the line joining P and Q, and A is equidistant from P and Q, A is the midpoint of P and Q.

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