Prove that the lines , , and form a rhombus.

Question

Philoid · Accepted Answer

Given: lines are as follows:

To prove:

lines form a rhombus.

Assuming:

In quadrilateral ABCD, let equations (1), (2), (3) and (4) represent the sides AB, BC, CD and

DA, respectively.

Explanation:

Lines (1) and (3) are parallel and lines (2) and (4) are parallel.

Solving (1) and (2):

x = 0, y = 0.

Thus, AB and BC intersect at B (0, 0).

Solving (1) and (4):

x , y

Thus, AB and DA intersect A

Solving (3) and (2):

x , y =

Thus, BC and CD intersect at C

Solving (3) and (4):

x , y

Thus, DA and CD intersect at D

Let us find the lengths of sides AB, BC and CD and DA.

AB

BC

CB

DA = 1

Hence Proved, the given lines form a rhombus.