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ad-work [718]
3 years ago
15

ABCD is a quadrilateral with A(8,21),B(10,27),C(26,26) and D(18,2). Determine whether ABCD is a trapizoid

Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
5 0
<h2>Answer:</h2>

ABCD is a trapezoid

<h2>Step-by-step explanation:</h2>

<em>Given points of the quadrilateral:</em>

A(8,21),B(10,27),C(26,26) and D(18,2)

To show whether ABCD is a trapezoid, we find a pair of parallel sides in ABCD. If two of its sides are parallel to each other then ABCD is a trapezoid.

<em>Step 1:</em> With the given points, sketch a graph. The diagram is attached to this response.

<em>Step 2:</em> As shown in the diagram, the two sides that are likely to be parallel are AB and CD

If these two sides have same gradient/slope, then the quadrilateral is a trapezoid.

Now calculate the slopes of those sides using the slope formula;

m = \frac{y_2 - y_1}{x_2 - x_1}

<em>Calculate the slope of AB </em>(where x₁ = 8, y₁ = 21, x₂ = 10, y₂ = 27)

m(AB) = \frac{27-21}{10-8}

m(AB) = \frac{6}{2}

m(AB) = 3

<em>Calculate the slope of CD </em>(where x₁ = 26, y₁ = 26, x₂ = 18, y₂ = 2)

m(CD) = \frac{2-26}{18-26}

m(CD) = \frac{-24}{-8}

m(CD) = 3

Since the two slopes - m(AB) and m(CD) slopes are equal to 3, the quadrilateral ABCD is a trapezoid.

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Binomial probability distribution

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