Question

Use coordinate geometry to determine the most precise name for the parallelogram with the given vertices. Credit will not be given if work is not shown. A(2, 5), B(7, 6), C(6, 2), and D(1, 1).

a) Rectangle
b) Rhombus
c) Trapezoid
d) Parallelogram

Answer 1

The most precise name for the parallelogram with the given vertices is a rectangle.

Step-by-step explanation:

The given coordinates of the vertices of the parallelogram are: A(2, 5), B(7, 6), C(6, 2), and D(1, 1). To determine the most precise name for the parallelogram, we need to check if the opposite sides are parallel and if the opposite sides are equal in length. We can use slope formula and distance formula to verify these conditions.

Using the slope formula, the slopes of the opposite sides AB and CD are equal, confirming that they are parallel. Similarly, the slopes of the opposite sides BC and AD are equal, indicating their parallelism as well.

Using the distance formula, we can calculate the lengths of the sides. The lengths of the opposite sides AD and BC are equal, as are the lengths of the sides AB and CD. Therefore, the most precise name for the parallelogram with the given vertices is a rectangle (option a) since all four angles are right angles and opposite sides are equal in length.