The given coordinates are actually a rectangle
How to determine the quadrilateral type?
The coordinates are given as:
A (3, 1), B (1, 5), C (9, 9), and D (11, 5).
Calculate the distance between the coordinates using:
[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(3 -1)^2 +(1-5)^2} =\sqrt {20[/tex]
[tex]BC = \sqrt{(1 -9)^2 +(5-9)^2} =\sqrt {80[/tex]
[tex]CD = \sqrt{(9 -11)^2 +(9-5)^2} =\sqrt {20[/tex]
[tex]DA = \sqrt{(11 -3)^2 +(5-1)^2} =\sqrt {80[/tex]
The above shows that the opposite sides are congruent
Next, we calculate the slopes using:
m = (y2- y1)/(x2- x1)
So, we have:
AB = (1- 5)/(3-1) = -2
BC = (5- 9)/(1-9) = 1/2
CD = (9- 5)/(9-11) = -2
DA = (5- 1)/(11-3) = 1/2
The slopes of adjacent sides are opposite reciprocals.
This means that the sides are perpendicular
Hence, the given coordinates are actually a rectangle
Read more about quadrilateral at:
https://brainly.com/question/16691874
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