Question

The coordinates of the vertices of quadrilateral ABCD are A(−1, −1) , B(−3, 3) , C(1, 5) , and D(5, 2) . Drag and drop the choices into each box to correctly complete the sentences. The slope of AB¯¯¯¯¯ is , the slope of BC¯¯¯¯¯ is , the slope of CD¯¯¯¯¯ is , and the slope of AD¯¯¯¯¯ is . Quadrilateral ABCD is because . −2−34122a parallelograma trapezoidneither a parallelogram nor a trapezoidboth pairs of opposite sides are parallelonly one pair of opposite sides is parallelneither pair of opposite sides is parallel

Answer 1

AB=-2
BC=1\2
CD=-3\4
AD=1\2

is that true or wrong

Answer 2

The slope of AB is - 2,

Slope of BC is
`(1)/(2)`

Slope of CD is
`-(3)/(4)`

Slope of AD is
`(1)/(2)`,

ABCD is trapezoid because one pair of opposite sides is parallel.

Explanation:

Given vertices of quadrilateral ABCD,

A(−1, −1) , B(−3, 3) , C(1, 5) , and D(5, 2),

∵ Slope of a line passes through two points
`(x_1, y_1)` and
`(x_2, y_2)` is,

`m=(y_2-y_1)/(xc_2-x_1)`

Thus, the slope of AB =
`(3+1)/(-3+1)=(4)/(-2)=-2`

Slope of BC =
`(5-3)/(1+3)=(2)/(4)=(1)/(2)`

Slope of CD =
`(2-5)/(5-1)=-(3)/(4)`

Slope of DA =
`(-1-2)/(-1-5)=(-3)/(-6)=(1)/(2)`

Since, when two line segment having the same slope then they are parallel to each other.

∴ BC ║ DA

A quadrilateral only having two parallel sides is called trapezoid,

Hence, ABCD is a trapezoid.