Question

Please answer one question asap
A(-4,3) B(2,-1) D(-4,-1) C(2,-5)

Answer 1

Explanation:

Vertices of the given quadrilateral are A(-4, 3), B(2, -1), C(2, -5) and D(-4, -1)

Since, slope of a line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by,

Slope =
`(y_2-y_1)/(x_2-x_1)`

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

=
`-(2)/(3)`

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

= Not defined (Parallel to y-axis)

Slope of DC =
`(-5+1)/(2+4)`

=
`-(2)/(3)`

Slope of BC =
`(-1+5)/(2-2)`

= Not defined (Parallel to y-axis)

Slope of AB = slope of DC =
`-(2)/(3)`

Slope of BC = slope of AD = Not defined (parallel to y-axis)

As per property of a parallelogram,

"Opposite sides of a parallelogram are parallel and equal in measure"

Therefore, ABCD is a parallelogram.