Question

show that the point A(5,6),B(1,5),C(2,1)and D(6,2) are the vertices of a square

Answer 1

Answer:

Given : A(5,6),B(1,5),C(2,1)and D(6,2)

To Find : show that the point A(5,6),B(1,5),C(2,1)and D(6,2) are the vertices of a square

Solution :

A(5,6),B(1,5),C(2,1)and D(6,2)

To show it square AB = BC = CD = AD

Use Distance formula : $d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$AB= \sqrt{(1-5)^2+(5-6)^2}$

$AB= 4.1231$

$BC= \sqrt{(2-1)^2+(1-5)^2}$

$BC= 4.1231$

$CD= \sqrt{(6-2)^2+(2-1)^2}$

$CD= 4.1231$

$AD= \sqrt{(6-5)^2+(2-6)^2}$

$AD= 4.1231$

Since AB =  BC = CD = AD

Hence it is a square .