Question

If A(1, 3), B(–1, 2), C(2, 5) and D(x, 4) are the vertices of a ||gm ABCD then the value of x is ______.

Options

• 3

• 4

• 0

• `3/2`

Answer 1

If A(1, 3), B(–1, 2), C(2, 5) and D(x, 4) are the vertices of a ||gm ABCD then the value of x is 4.

Explanation:

Midpoint theorem method

In a parallelogram ABCD, the diagonals AC and BD bisect each other. This means that the midpoint of diagonal AC is identical to the midpoint of diagonal BD.

The formula for the midpoint between two points (x₁, y₁) and (x₂, y₂) is:

Midpoint = `((x_1 + x_2)/2, (y_1 + y_2)/2)`

X-coordinate of the midpoint of AC:

`(1 + 2)/2 = 3/2`

X-coordinate of the midpoint of BD:

`(-1 + x)/2`

Equating the x-coordinates of both midpoints:

`3/2 = (-1 + x)/2`

Multiplying both sides by 2:

3 = –1 + x

x = 3 + 1

x = 4