Question

Select all of the names that can be given to the shape ABCD with the vertices A(3, 4), B(2, 1), C(-4, - 2), and D(-3, 1).

quadrilateral


trapezoid


rhombus


square


rectangle


parallelogram

Answer 1

quadrilateral, trapezoid, parallelogram

Explanation:

AB =
`√((3-2)^2 + (4-1)^2) = √(1^2 + 3^2) = √(1 + 9) = √(10)`

BC =
`√((-4-2)^2+(-2-1)^2) = √((-6)^2 + (-3)^2) = √(36 + 9) = \sqrt{45`

CD =
`√((-3+4)^2 + (1+2)^2) = √(1^2 + 3^2) = √(1+9) = √(10)`

AD =
`√((-3-3)^2 + (1-4)^2) = √((-6)^2 + (-3)^2) = √(36+9) = √(45)`

slope of AB = (1-4)/(2-3) = -3/-1 = 3

slope of CD = (1+2)/(-3+4) = 3/1 = 3

slope of BC = (-2-1)/(-4-2) = -3/-6 = 1/2

slope of AD = (1-4)/(-3-3) = -3/-6 = 1/2

four sides: quadrilateral

parallel bases : trapezoid

two couple of equal parallel sides: parallelogram