Question

What kind of shape has vertices `A(-1, -4), B(1, -1), C(4,1), D(2, -2)`?

Answer 1

Shape of the figure is a SQUARE

Explanation:

`A(-1,-4), B(1,-1), C(4,1), D(2,-2)`

Slope of `bar(AB) = (-1+4) / (1 + 1) = 3/2`

Slope of `bar (CD) = (-2-1) / (2-4) = 3/2`

Slope of `bar(BC) = (1+1)/(4-3) = -2/3`

Slope of `bar (AD) = (-2+4) / (2+1) = -2/3`

`vec(AB)` “parallel “ `vec(CD), vec(BC)` “ parallel “ `vec(AD)`

`vec(AB)` “ perpendicular “ `vec(BC)`, `vec(CD)` “ perpendicular “ vec(AD)#

`vec(AB) = sqrt((1+1)^2 + (-1+4)^2) = sqrt13`

`vec(BC) = sqrt((4-1)^2 + (1+1)^2) = sqrt13`

Hence `vec(AB) = vec(BC)`

Therefore the shape of the figure is a SQUARE