If (–2, –1), (1, 0) and (4, 3) are the successive vertices of a parallelogram then the fourth vertex is

To find the fourth vertex of a parallelogram, we can use the property of a parallelogram that opposite sides are equal.

Given the vertices are (–2, –1), (1, 0) and (4, 3). Let's assume the fourth vertex is (x, y).

We know that diagonals of a parallelogram bisect each other. So, the mid-point of the diagonal joining (–2, –1) and (4, 3) should be the same as the mid-point of the diagonal joining (1, 0) and (x, y).

The mid-point of (–2, –1) and (4, 3) is ((–2+4)/2, (–1+3)/2) = (1, 1).

Let's equate this to the mid-point of (1, 0) and (x, y), which is ((1+x)/2, (0+y)/2).

So, we have:

(1+x)/2 = 1 and (0+y)/2 = 1.

Solving these equations, we get x = 1 and y = 2.

So, the fourth vertex of the parallelogram is (1, 2).