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<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 =
<em>Calculate the slope of AB </em>(where x₁ = 8, y₁ = 21, x₂ = 10, y₂ = 27)
m(AB) =
m(AB) =
m(AB) = 3
<em>Calculate the slope of CD </em>(where x₁ = 26, y₁ = 26, x₂ = 18, y₂ = 2)
m(CD) =
m(CD) =
m(CD) = 3
Since the two slopes - m(AB) and m(CD) slopes are equal to 3, the quadrilateral ABCD is a trapezoid.