Question

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

Answer 1

ABCD is a trapezoid

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 =
`(y_2 - y_1)/(x_2 - x_1)`

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

m(AB) =
`(27-21)/(10-8)`

m(AB) =
`(6)/(2)`

m(AB) = 3

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

m(CD) =
`(2-26)/(18-26)`

m(CD) =
`(-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.