What is the most precise name for quadrilateral ABCD with vertices A(-3 2), B(-1 4), C(4 4), and D(2 2)?
Parallelogram
Rhombus
quadrilateral
rectangle
Pls help ASAP
To determine the most precise name for the given quadrilateral ABCD, let's analyze the properties of different quadrilaterals based on their sides and angles.
1. Parallelogram: A parallelogram is a quadrilateral with opposite sides being parallel. To check if ABCD is a parallelogram, we need to compare the slopes of opposite sides BC and AD, as well as AB and CD. However, calculating the slopes requires finding the equation of the lines passing through the given points and their corresponding slopes. This can be done using the formula: slope (m) = (change in y) / (change in x). Then we can compare the slopes to determine if the quadrilateral has opposite sides that are parallel.
2. Rhombus: A rhombus is a quadrilateral with all four sides having equal lengths. To determine if ABCD is a rhombus, we need to measure the distance between each pair of adjacent points (A,B), (B,C), (C,D), and (D,A) using the distance formula: distance = √[(x2 - x1)^2 + (y2 - y1)^2]. If all four distances are equal, then ABCD is a rhombus.
3. Rectangle: A rectangle is a quadrilateral with all interior angles equaling 90 degrees. To check if ABCD is a rectangle, we need to find the slopes of the lines containing the sides AB, BC, CD, and DA. If the product of the slopes of opposite sides is -1, then ABCD is a rectangle.
4. Quadrilateral: If none of the above conditions (parallelogram, rhombus, or rectangle) are met, the most general term for the quadrilateral ABCD is simply "quadrilateral."
To get a definitive answer on the most precise name for the given quadrilateral, you will need to calculate the slopes and distances as described above.