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 = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
So,
AB = [tex]\sqrt{(4-3)^2+(4-1)^2} =\sqrt{10}[/tex]
BC = [tex]\sqrt{(4-7)^2+(4-5)^2} =\sqrt{10}[/tex]
CD = [tex]\sqrt{(7-6)^2+(5-2)^2} =\sqrt{10}[/tex]
DA = [tex]\sqrt{(3-6)^2+(1-2)^2} =\sqrt{10}[/tex]
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.
The name of the quadrilateral with the given coordinates is; D: rhombus, because all four sides are congruent and adjacent sides are not perpendicular
Formula for distance between two coordinates is;
D = √[(y2 - y1)² + (x2 - x1)²]
Thus;
AB = √(9 + 1)
AB = √10
BC = √(1 +9)
BC = √10
CD = √(9 +1)
CD = √10
AD = √(1 +9)
AD = √10
Now, this means that the four sides are equal and as such it may be a rhombus or a square.
However, from the image of the quadrilateral attached, we can see that the four sides are not perpendicular and as such the quadrilateral ABCD is a rhombus.
Read more about Rhombus at; https://brainly.com/question/20627264
