Question

Show from the gradients that the points (4,1),(1,2),(2,5) and (5,4) are the vertices of a square.
(This question is from the chapter Co-ordinate geometry)
Please help me to solve this and no spams please or else the answer will be reported ​

Answer 1

Let the vertices are

M(4,1), N(1,2), R(2,5), Q(5,4)

MN = √(4-1)^2 + (1-2)^2

= √(3)^2 + (-1)^2

= √(9) + (1)

= √(10)

NR = √(1-2)^2 + (2-5)^2

= √(-1)^2 + (-3)^2

= √(1) + (9)

= √(10)

RQ = √(2-5)^2 + (5-4)^2

= √(-3)^2 + (1)^2

= √(9) + (1)

= √(10)

MQ = √(4-5)^2 + (1-4)^2

= √(-1)^2 + (-3)^2

= √(1)+ (9)

= √(10)

all sides are equal, Hence MNRQ is a square