The most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8), and D(8, 5) is a right trapezoid.
To determine this, we need to analyze the sides and angles of the quadrilateral. First, let’s look at the coordinates:
- A(4, 4)
- B(5, 8)
- C(8, 8)
- D(8, 5)
The line segments BC and AD are parallel because they share the same y-coordinates (y = 8 for C and B; y = 4 and y = 5 for D and A). This property indicates that ABCD could be a trapezoid. Next, we need to look at the angles: angle B and angle D are both right angles, making this quadrilateral not just any trapezoid, but a right trapezoid.
Moreover, the lengths of the sides can be calculated:
- AB: from A(4, 4) to B(5, 8)
- BC: from B(5, 8) to C(8, 8)
- CD: from C(8, 8) to D(8, 5)
- DA: from D(8, 5) to A(4, 4)
By examining the lengths and seeing the configuration, it’s clear that ABCD has one pair of parallel sides and two right angles. Therefore, the classification of the quadrilateral ABCD is most accurately described as a right trapezoid.