Answer:
Step-by-step explanation:
A (1 ,7) , B(4, 2), C(-1, -1) and D(-4, 4)
Find the distance of sides using distance formula.
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
A (1 ,7) , B(4, 2)
[tex]AB = \sqrt{(4-1)^{2}+(2-7)^{2}}\\\\ =\sqrt{3^{2}+(-5)^{2}}\\\\ \\ = \sqrt{9+25}=\sqrt{34} units\\\\\\\\BC = \sqrt{(-1-4)^{2}+(-1-2)^{2}}\\\\ =\sqrt{(-5)^{2}+(-3)^{2}} = \sqrt{25+9}=\sqrt{34} units\\\\\\CD = \sqrt{(-4-[-1])^{2}+(4-[-1])^{2}}\\\\=\sqrt{(-4+1)^{2}+(4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(5)^{2}}\\\\=\sqrt{9+25} = \sqrt{34} units\\\\\\AD = \sqrt{(-4-1)^{2}+(4-7)^{2}}\\\\=\sqrt{(-5)^{2}+(-3)^{2}} =\sqrt{25+9} = \sqrt{34} units[/tex]
AB = BC = CD = AD = √34 units. so , ABCD is a square.
Area of square = side * side
= √34 * √34
= 34 square units
