Question

If \( A (3, 0), B (4,5), C (-1,4) \) and \( D (-2,-1) \) be four points in a plane, then the quadrilateral ABCD represents

1) Rhombus

2) Square

3) Parallelogram

4) Kite

Answer 1

The correct option is (1) Rhombus

Let the points of rhombus are A(3, 0), B(4, 5), C(-1, 4) and D(-2, -1).

So by distance formula we have,

Distance between two points = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

∴ AB = BC = CD = AD = √26

We know that all the sides of a rhombus are Equal.

∴ ABCD is a rhombus.