The most precise name for the quadrilateral ABCD with the given vertices is a trapezoid.
To explain, we need to analyze the coordinates of the points:
- A(3, 2)
- B(1, 4)
- C(4, 4)
- D(2, 2)
First, let’s plot these points on a coordinate system. When we connect the points in the order A, B, C, D, we can observe the shape formed by these vertices.
Next, we calculate the slopes of the sides AB, BC, CD, and DA:
- AB: Slope = (y2 – y1) / (x2 – x1) = (4 – 2) / (1 – 3) = 2 / -2 = -1
- BC: Slope = (4 – 4) / (4 – 1) = 0 / 3 = 0
- CD: Slope = (2 – 4) / (2 – 4) = -2 / -2 = 1
- DA: Slope = (2 – 2) / (3 – 2) = 0 / 1 = 0
From this, we see that sides BC and DA are both horizontal, which means they are parallel lines. Since we have at least one pair of opposite sides that are parallel, this confirms that quadrilateral ABCD is a trapezoid.
Therefore, the most precise name for quadrilateral ABCD is a trapezoid.