Question

Three consecutive vertices of a parallelogram are (-2,-1),(1,0) and (4,3) find the fourth vertex

Answer 1

The Diagonals of a parallelogram bisect each other.

Given,

Vertices of the parallelogram are

A (-2,-1)

B (1,0)

C (4,3)

Let the fourth vertex be D(x, y)

The Diagonals of the parallelogram are AC, BD.

As the Diagonals bisect each other,

Mid point of AC = Mid point of BD

Mid point of a line joining two points L(x, y) & K ( a, b) is

$\boxed{ \frac{x + a}{2} \frac{y + b}{2} }$

So,

$\bigg( \frac{ - 2 + 4}{2} ,\frac{ - 1 + 3}{2} \bigg) = \bigg(\frac{1 + x}{2} , \frac{0 + y}{2} \bigg)$

Comparing the X - Coordinate :

$\frac{ - 2 + 4}{2} = \frac{1 + x}{2} \\ \\ - 2 + 4 = 1 + x \\ \\ \: \: \: \: \: \: \: \: \: \: \: 2 = 1 + x \\ \\ \: \: \: \: \: \: \: \: \: \: \: x = 2 - 1 \\ \\ \: \: \: \: \: \: \: \: \: \: \: x = 1$

Comparing the Y - Coordinate

$\frac{ - 1 + 3}{2} = \frac{0 + y}{2} \\ \\ - 1 + 3 = 0 + y \\ \\ \: \: \: \: \: \: \: \: \: \: \: y = 2$

Therefore, The fourth vertex is (1,2)

Answer 2

Answer:

D = (1, 2)

Step-by-step explanation:

The diagonals of parallelogram bisect each other, so find the coordinate of the midpoint in two ways,

Once with the help of A and C, and the second time with the help of B and D. Equate them, to find the coordinates of D(x, y).

Check out the attachment for the solution.

Thanks!