a. Prove that R(2,1), E(10,7), C(7,11) and T(­1,5) are the vertices of a rectangle. b. Prove that this rectangle is not a square.

Question

a. Prove that R(2,1), E(10,7), C(7,11) and T(­1,5) are the vertices of a rectangle.

b. Prove that this rectangle is not a square.

Answer 1

RT = sqr(1+16)=sqr17

RE= sqr(64+36)=10

TC=sqr(36+36)=6sqr2

EC=sqr(9+16)=5

to be a square all 4 sides would be equal. They aren't, using the distance formula, with d^2 = a^2+b^2

d=sqr(a^2+b^2 where a and b are the difference in x coordinates and difference in y coordinates.

It's not a rectangle either, as a rectangle has 2 sides the same, and the other 2 sides also the same.

It is a quadrilateral, a 4 sided polygon