Question

Given the coordinates of the vertices of a quadrilateral, determine whether it is a square, a rectangle, or a parallelogram. Then find the perimeter of the quadrilateral. A(6, –4), B(11, –4), C(11, 6), D(6, 6)

Answer 1

To determine the shape of the quadrilateral, calculate the distances between the vertices and check for equal side lengths and 90-degree angles. The given quadrilateral is a parallelogram since the opposite sides are parallel and equal. The perimeter of the quadrilateral is 30 units.

Step-by-step explanation:

To determine whether the given quadrilateral is a square, a rectangle, or a parallelogram, we can use the properties of each shape. A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees. A rectangle is a quadrilateral with opposite sides equal in length and all angles equal to 90 degrees. A parallelogram is a quadrilateral with opposite sides parallel and equal in length. To find the perimeter of the quadrilateral, we can calculate the sum of the lengths of all four sides.

Calculating the distances between each pair of given points:

• Distance between A and B: √[(11-6)² + (-4-(-4))²] = √(5² + 0) = √25 = 5
• Distance between B and C: √[(11-11)² + (6-(-4))²] = √(0 + 100) = 10
• Distance between C and D: √[(6-11)² + (6-6)²] = √((-5)² + 0) = √25 = 5
• Distance between D and A: √[(6-6)² + (6-(-4))²] = √(0 + 100) = 10

The distances between the vertices are: AB = 5, BC = 10, CD = 5, and DA = 10. Therefore, the perimeter of the quadrilateral is 5 + 10 + 5 + 10 = 30 units.

Answer 2

The answer to your question is: it's a rectangle

perimeter = 30 u

Step-by-step explanation:

d = √((x2.x1)² + (y2-y1)²)

Now, calculate the distances AB, BC, CD, AD

dAB = √((11-6)² + (-4+4)² = √5² = 5

dBC = √((11-11)² + (-4-6)² =√10 = 10

dCD = √((6-11)² + (6-6)² = √5² = 5

dAD = √((6-6)² + (6+4)² = √10² = 10

From the results we conclude that is a rectangle because two sides have the same length and the other two also measure the same. We can draw it to confirm this.

Perimeter = dAB + dBC + dCD + dAD

= 5 + 10+ 5 + 10 = 30 units