Question

show that the points (1 ,7) ,(4, 2), (-1, -1) and (-4, 4) taken in order are the vertics of a square. Also find its area

Answer 1

Explanation:

A (1 ,7) , B(4, 2), C(-1, -1) and D(-4, 4)

Find the distance of sides using distance formula.

Distance =
`\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`

A (1 ,7) , B(4, 2)

`AB = \sqrt{(4-1)^(2)+(2-7)^(2)}\\\\ =\sqrt{3^(2)+(-5)^(2)}\\\\ \\ = √(9+25)=√(34) units\\\\\\\\BC = \sqrt{(-1-4)^(2)+(-1-2)^(2)}\\\\ =\sqrt{(-5)^(2)+(-3)^(2)} = √(25+9)=√(34) units\\\\\\CD = \sqrt{(-4-[-1])^(2)+(4-[-1])^(2)}\\\\=\sqrt{(-4+1)^(2)+(4+1)^(2)}\\\\=\sqrt{(-3)^(2)+(5)^(2)}\\\\=√(9+25) = √(34) units\\\\\\AD = \sqrt{(-4-1)^(2)+(4-7)^(2)}\\\\=\sqrt{(-5)^(2)+(-3)^(2)} =√(25+9) = √(34) units`

AB = BC = CD = AD = √34 units. so , ABCD is a square.

Area of square = side * side

= √34 * √34

= 34 square units