Question

If a line segment joining the points P and Q $(3, -4)$ is bisected at origin, then the coordinates of P are :

• A. $(4, -3)$
• B. $(2, 4)$
• C. $(-3, 4)$
• D. $(4, 3)$

Hint:

When a line segment is bisected at a point, that point is the midpoint of the segment. The origin $(0,0)$ acts as the midpoint here. Understanding the midpoint formula is crucial for solving this problem.

Answer 1

The Correct Option is C

Step 1: Understand the given information and define coordinates.
Let the coordinates of point P be $(x_1, y_1)$.
Let the coordinates of point Q be $(x_2, y_2) = (3, -4)$.
The line segment PQ is bisected at the origin. This means the origin $(0, 0)$ is the midpoint of the line segment PQ.
Step 2: Recall the midpoint formula.
The midpoint M of a line segment joining two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ Step 3: Apply the midpoint formula with the given information.
Here, the midpoint M is the origin $(0, 0)$.
So, we have:
$(0, 0) = \left(\frac{x_1 + 3}{2}, \frac{y_1 + (-4)}{2}\right)$ Step 4: Equate the x-coordinates and y-coordinates to find $x_1$ and $y_1$.
For the x-coordinate:
$\frac{x_1 + 3}{2} = 0$
$x_1 + 3 = 0 \times 2$
$x_1 + 3 = 0$
$x_1 = -3$
For the y-coordinate:
$\frac{y_1 - 4}{2} = 0$
$y_1 - 4 = 0 \times 2$
$y_1 - 4 = 0$
$y_1 = 4$
Step 5: State the coordinates of P.
The coordinates of point P are $(-3, 4)$. Step 6: Compare with the given options.
The calculated coordinates are $(-3, 4)$, which matches option (3). (3) $(-3, 4)$