Question

If the points A(5, 3), B(8, 5), C(x, y) and D(7, 2) are consecutive vertices of a parallelogram then (x, y) = A(5, 3), B(8, 5), C(x, y)=

• A. (4,0)
• B. (4, 4)
• C. (10, 4)
• D. (4,3)

Answer 1

The Correct Option is C

Let’s assume the order of the parallelogram vertices is A → B → C → D. In a parallelogram, the diagonals bisect each other. So, the midpoint of AC must be equal to the midpoint of BD. Coordinates of A = (5, 3), C = (x, y) Coordinates of B = (8, 5), D = (7, 2) Midpoint of AC = \( \left( \frac{5 + x}{2}, \frac{3 + y}{2} \right) \) Midpoint of BD = \( \left( \frac{8 + 7}{2}, \frac{5 + 2}{2} \right) = (7.5, 3.5) \) Equating both midpoints: \[ \frac{5 + x}{2} = 7.5 \Rightarrow 5 + x = 15 \Rightarrow x = 10 \] \[ \frac{3 + y}{2} = 3.5 \Rightarrow 3 + y = 7 \Rightarrow y = 4 \]

The correct option is (C): \((10, 4)\)