Answer:
ABCD is a trapezoid
Step-by-step explanation:
Given points of the quadrilateral:
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.
Step 1: With the given points, sketch a graph. The diagram is attached to this response.
Step 2: 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 = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Calculate the slope of AB (where x₁ = 8, y₁ = 21, x₂ = 10, y₂ = 27)
m(AB) = [tex]\frac{27-21}{10-8}[/tex]
m(AB) = [tex]\frac{6}{2}[/tex]
m(AB) = 3
Calculate the slope of CD (where x₁ = 26, y₁ = 26, x₂ = 18, y₂ = 2)
m(CD) = [tex]\frac{2-26}{18-26}[/tex]
m(CD) = [tex]\frac{-24}{-8}[/tex]
m(CD) = 3
Since the two slopes - m(AB) and m(CD) slopes are equal to 3, the quadrilateral ABCD is a trapezoid.
