Question

Quadrilateral ABCD has coordinates A (3, 1), B (4,4), C (7,5), D (6,2). Quadrilateral ABCD is a

Answer 1

Answer:

Quadrilateral ABCD is a rhombus, because all four sides are congruent and adjacent sides are not perpendicular .

Step-by-step explanation:

Given :

A quadrilateral with its coordinates as follows:

Where  A (3, 1), B (4,4), C (7,5), D (6,2).

We will measure the length of the congruent sides by applying distance formula.

Distance formula = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

So,

AB = $\sqrt{(4-3)^2+(4-1)^2} =\sqrt{10}$

BC = $\sqrt{(4-7)^2+(4-5)^2} =\sqrt{10}$

CD = $\sqrt{(7-6)^2+(5-2)^2} =\sqrt{10}$

DA = $\sqrt{(3-6)^2+(1-2)^2} =\sqrt{10}$

From the above measurement and looking into the diagram we can conclude that the Quadrilateral ABCD is a rhombus.

In rhombus the adjacent sides are not perpendicular and its diagonals are of different length.

Option D is the correct choice.