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Question

# Find the midpoint of the line joining P(3, 3) and Q(3, -3).

A
(3, 0)
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B
(0, 3)
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C
(3, 3)
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D
(0, 0)
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Solution

## The correct option is A (3, 0) 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. ∵ Distance between two points (x1,y1) and (x2,y2)=√(x2−x1)2+(x2−y1)2 ∴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 midpoint of P and Q.

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