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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

Respuesta :

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

is that true or wrong

Answer:

The slope of AB is - 2,

Slope of BC is [tex]\frac{1}{2}[/tex]

Slope of CD is [tex]-\frac{3}{4}[/tex]

Slope of AD is [tex]\frac{1}{2}[/tex],

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

Step-by-step 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 [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,

[tex]m=\frac{y_2-y_1}{xc_2-x_1}[/tex]

Thus, the slope of AB = [tex]\frac{3+1}{-3+1}=\frac{4}{-2}=-2[/tex]

Slope of BC = [tex]\frac{5-3}{1+3}=\frac{2}{4}=\frac{1}{2}[/tex]

Slope of CD = [tex]\frac{2-5}{5-1}=-\frac{3}{4}[/tex]

Slope of DA = [tex]\frac{-1-2}{-1-5}=\frac{-3}{-6}=\frac{1}{2}[/tex]

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.