Question

Prove that the points(4,-1),(6,0),(7,2)&(5,1) are the vertices of a rhombus.Is it a square?

Answer 1

$<i><b>Heya!!!$

Answer to your question:

Let A (4,-1) B (6,0) C (7,2) and D (5,1)
Length of sides :
AB=root {(2)^2+(1)^2}=root5
BC=root {(1)^2+(2)^2}=root5
CD=root {(2)^2+(1)^2}=root5
AD=root {(1)^2+(2)^2}=root5

We get,
AB=BC=CD=AD
hence ABCD is rhombus

now AC=root {(3)^2+(3)^2}=3root2
here AC^2=BC^2+CA^2 isn't possible so
ABCD isn't square this is only rhombus.

Hope it helps ^_^