Determine whether quadrilateral abcd with vertices a(–4, –5), b(–3, 0), c(0, 2), and d(5, 1) is a trapezoid. step 1: find the slope of ab. the slope of ab is . step 2: find the slope of dc. the slope of dc is . step 3: find the slope of bc. the slope of bc is . step 4: find the slope of ad. the slope ad is . the quadrilateral is a trapezoid because

All the  slope of quadrilateral ABCD  calculated by using formula of slope.

Given:

A quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).

We have to calculate the slope of AB, DC, BC, AD.

By using formula of slope,

Now, calculate the slope of AB,

A(–4, –5), B(–3, 0), put this value in (1)

Calculate the slope of DC,

C(0, 2), D(5, 1), put this value in (1)

Calculate the slope of BC,

B(–3, 0), C(0, 2), put this value in (1)

Calculate the slope of AD,

A(–4, –5), D(5, 1), put this value in (1)

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1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.