Graph quadrilateral ABCD. Then determine the most precise name for each quadrilateral.

1. A (0, 5), B (–5, 0), C (0, –5), D (5, 0) (1 point)
square
kite
rectangle
2. A (–4, 4), B (3, 4), C (5, 0), D (–2, 0) (1 point)
square
trapezoid
parallelogram
3. A (6, 10), B (9, 8), C (6, 2), D (3, 8) (1 point)
kite
square
trapezoid
4. A (–3, 5), B (1, 7), C (3, 2), D (–7, –3) (1 point)
parallelogram
trapezoid
rectangle

If you graph the points on a graph paper (which we cannot do here) it should become clear what the quadrilaterals are.

1. Kite

2. parallelogram
3. Kite
4. trapezoid

To graph quadrilateral ABCD for each question:

1. Plot the points A (0, 5), B (–5, 0), C (0, –5), and D (5, 0) on a graph. Connect the points in the order given to form the quadrilateral.

2. Plot the points A (–4, 4), B (3, 4), C (5, 0), and D (–2, 0) on a graph. Connect the points in the order given to form the quadrilateral.

3. Plot the points A (6, 10), B (9, 8), C (6, 2), and D (3, 8) on a graph. Connect the points in the order given to form the quadrilateral.

4. Plot the points A (–3, 5), B (1, 7), C (3, 2), and D (–7, –3) on a graph. Connect the points in the order given to form the quadrilateral.

Now let's determine the most precise name for each quadrilateral:

1. The quadrilateral formed by the points A (0, 5), B (–5, 0), C (0, –5), and D (5, 0) is a square since all four sides are equal in length and the angles are all right angles.

2. The quadrilateral formed by the points A (–4, 4), B (3, 4), C (5, 0), and D (–2, 0) is a trapezoid since it has only one pair of parallel sides.

3. The quadrilateral formed by the points A (6, 10), B (9, 8), C (6, 2), and D (3, 8) is a kite since it has two pairs of adjacent sides that are equal in length.

4. The quadrilateral formed by the points A (–3, 5), B (1, 7), C (3, 2), and D (–7, –3) is a parallelogram since opposite sides are parallel.

So, the most precise name for each quadrilateral is:

1. Square
2. Trapezoid
3. Kite
4. Parallelogram

To determine the most precise name for each quadrilateral, we need to analyze the properties of each quadrilateral.

1. Quadrilateral ABCD:
Plot the points A(0, 5), B(-5, 0), C(0, -5), and D(5, 0) on a graph. Join the points to form a quadrilateral.

Based on the given coordinates, the sides AB, BC, CD, and DA are all equal in length. Additionally, all angles in the quadrilateral are right angles (90 degrees).

Therefore, quadrilateral ABCD is a square.

2. Quadrilateral ABCD:
Plot the points A(-4, 4), B(3, 4), C(5, 0), and D(-2, 0) on a graph. Join the points to form a quadrilateral.

In this case, the opposite sides AB and CD are parallel and of equal length. Also, the opposite sides AD and BC are parallel but not of equal length. The adjacent angles are equal in measure, but not all angles are right angles.

Therefore, quadrilateral ABCD is a trapezoid.

3. Quadrilateral ABCD:
Plot the points A(6, 10), B(9, 8), C(6, 2), and D(3, 8) on a graph. Join the points to form a quadrilateral.

In this case, the opposite sides AB and CD are not parallel. The adjacent sides AD and BC are parallel. Additionally, the adjacent angles are equal in measurement but not all angles are right angles.

Therefore, quadrilateral ABCD is a kite.

4. Quadrilateral ABCD:
Plot the points A(-3, 5), B(1, 7), C(3, 2), and D(-7, -3) on a graph. Join the points to form a quadrilateral.

In this case, the opposite sides AB and CD are parallel. The adjacent sides AD and BC are also parallel. Additionally, the opposite angles are equal in measurement, but not all angles are right angles.

Therefore, quadrilateral ABCD is a parallelogram.

Based on the given coordinates and properties of quadrilaterals, the most precise names for the given quadrilaterals are:
1. Quadrilateral ABCD: Square
2. Quadrilateral ABCD: Trapezoid
3. Quadrilateral ABCD: Kite
4. Quadrilateral ABCD: Parallelogram