Area Of A Parallelogram

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 = Midpoint of BD = Equating both midpoints:

The correct option is (C):

Given:

The vertices of a parallelogram are (-3, -1), (a, b), (3, 3), and (4, 3), taken in order.

Step 1: Use the property of the midpoint of diagonals.

In a parallelogram, the diagonals bisect each other. Therefore, the midpoints of both diagonals are the same.

The midpoint of the diagonal joining (-3, -1) and (3, 3) can be calculated as:

Midpoint =

The midpoint of the diagonal joining (a, b) and (4, 3) is:

Midpoint =

Step 2: Set the midpoints equal to each other.

Since the midpoints of the diagonals are the same, we can equate the two midpoints:

Step 3: Solve for a and b.

From the x-coordinates: , which gives , so .

From the y-coordinates: , which gives , so .

Step 4: Find the ratio of a and b.

The ratio of a and b is:

Answer: The ratio of a and b is 4 : 1.

Given: The diagonals of a rhombus are 24 cm and 10 cm.

Step 1: Understanding the properties of a rhombus

In a rhombus, the diagonals bisect each other at right angles.

Let the diagonals be cm and cm.

Each diagonal is divided into two equal halves:

Step 2: Apply Pythagoras Theorem

Each side of the rhombus forms a right-angled triangle with half-diagonals as legs:

Final Answer: 13 cm