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
• B. False

Answer 1

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.
$AP=\sqrt{(3-3{)}^2+(3-0{)}^2}=3---------------\left(1\right)AQ=\sqrt{(3-3{)}^2+(-3-\left(0\right){)}^2}=3---------------\left(2\right)$

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.