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Question

# For the figure given below, A(3, 0) is the midpoint of the line joining P(3, 3) and Q(3, -3).

A

True

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B

False

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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=√(3−3)2+(3−0)2=3−−−−−−−−−−−−−−− (1)AQ=√(3−3)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 mid point of P and Q.

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