Answer:
The answer to your question is Yes, it is a square.
Step-by-step explanation:
Data
From the picture
A (8, 3)
B (7, 8)
C (2, 7)
D (3, 2)
Process
-Use the formula of the distance between two points.
-Calculate the distance between AB, BC, CD, DA
Formula
d = [tex]\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2}}[/tex]
1.- Distance between AB
dAB = [tex]\sqrt{(7 - 8)^{2}+ (8 - 3)^{2}}[/tex]
dAB = [tex]\sqrt{(-1)^{2}+ (5)^{2}}[/tex]
dAB = [tex]\sqrt{1 + 25}[/tex]
dAB = [tex]\sqrt{26}[/tex]
2.- Distance between BC
dBC = [tex]\sqrt{(2 - 7)^{2}+ (7 - 8)^{2}}[/tex]
dBC = [tex]\sqrt{(-5)^{2}+ (-1)^{2}}[/tex]
dBC = [tex]\sqrt{25 + 1}[/tex]
dBC = [tex]\sqrt{26}[/tex]
3.- Distance between CD
dCD = [tex]\sqrt{(3 - 2)^{2}+ (2 - 7)^{2}}[/tex]
dCD = [tex]\sqrt{(1)^{2}+ (5)^{2}}[/tex]
dCD = [tex]\sqrt{1 + 25}[/tex]
dCD = [tex]\sqrt{26}[/tex]
4.- Distance between AD
dAD = [tex]\sqrt{(3 - 8)^{2}+ (2 - 3)^{2}}[/tex]
dAD = [tex]\sqrt{(-5)^{2}+ (-1)^{2}}[/tex]
dAD = [tex]\sqrt{25 + 1}[/tex]
dAD = [tex]\sqrt{26}[/tex]
5.- Conclusion
The quadrilateral ABCD is a square because dAB = dBC = dCD = dDA
