Answer:
It is a trapezoid
Explanation:
Yes, the given points represent the vertices of a trapezoid.
A trapezoid is a quadrilateral with one set of parallel sides. In this case, the parallel sides are AB and CD. The other two sides, AD and BC, are not parallel.
The trapezoid is not isosceles because the two non-parallel sides are not congruent. AD has a length of 6 units, while BC has a length of 4 units.
Here is a diagram of the trapezoid:
A(-4,-1)
B((-4,6)
C(2,6)
D(2,-4)
A trapezoid is a quadrilateral with at least one pair of parallel sides. In this case, sides AB and CD are parallel because they have the same slope. So, the given points do represent the vertices of a trapezoid.
An isosceles trapezoid has two congruent legs (non-parallel sides). In this case, the length of side AD is `sqrt((-4-2)^2+(-1+4)^2)=sqrt(36+9)=sqrt(45)` and the length of side BC is `sqrt((-4-2)^2+(6-6)^2)=sqrt(36+0)=sqrt(36)`. Since `sqrt(45)` is not equal to `sqrt(36)`, the trapezoid is not isosceles.