Question

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

• A. (3, 0)
• B. (0, 3)
• C. (3, 3)
• D. (0, 0)

Answer 1

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.

$\because$ Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$$=\sqrt{(x_2-x_1{)}^2+(x_2-y_1{)}^2}$
$\therefore AP=\sqrt{(3-3{)}^2+(3-0{)}^2}=3---\left(1\right)AQ=\sqrt{(3-3{)}^2+(-3-\left(0\right){)}^2}=3---\left(2\right)$

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 midpoint of P and Q.