Question

If the points A (6, 1), B (8, 2), C (9, 4) and D (7, 3) are the vertices of a parallelogram, taken in order, the point of intersection of diagonals will be :

• A. (15/2, 5/2)
• B. (15/2, 5)
• C. (7/2, 5)
• D. (5, 15/2)

Hint:

You only need to find the midpoint of one diagonal (AC or BD) because they share the same intersection point in a parallelogram!

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In a parallelogram, the diagonals bisect each other. This means the midpoint of diagonal $AC$ is the same as the midpoint of diagonal $BD$. This common midpoint is the point of intersection.

Step 2: Midpoint Formula:
The midpoint $(x, y)$ of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$$x = \frac{x_1 + x_2}{2}, \quad y = \frac{y_1 + y_2}{2}$$
Step 3: Calculation for diagonal AC:
Using points $A(6, 1)$ and $C(9, 4)$:
$$x = \frac{6 + 9}{2} = \frac{15}{2}$$
$$y = \frac{1 + 4}{2} = \frac{5}{2}$$
Step 4: Final Answer:
The point of intersection is (15/2, 5/2). (Note: Option A was corrected from the original typo in the prompt).