Given Quadrilateral ABCD and the points A(-2,6), B(4,6), C(4,-3) and D(-2,-3). What are the lengths of each side, and what is the most specific name for this polygon.
looks like a 6x9 rectangle to me
Determine whether ABCD is a reactangle given each set of vertices. Justify your answer.
1. A(-3,1), B(-3,3), C(3,3), D(3,1)
To find the lengths of the sides of the quadrilateral ABCD, we can use the distance formula. The distance formula states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = sqrt((x₂ - x₁)² + (y₂ - y₁)²)
Let's calculate the lengths of each side:
Side AB:
dAB = sqrt((4 - (-2))² + (6 - 6)²)
= sqrt(6² + 0²)
= sqrt(36 + 0)
= sqrt(36)
= 6
Side BC:
dBC = sqrt((4 - 4)² + (-3 - 6)²)
= sqrt(0² + (-9)²)
= sqrt(0 + 81)
= sqrt(81)
= 9
Side CD:
dCD = sqrt((-2 - 4)² + (-3 - (-3))²)
= sqrt((-6)² + 0²)
= sqrt(36 + 0)
= sqrt(36)
= 6
Side DA:
dDA = sqrt((-2 - (-2)² + (-3 - 6)²)
= sqrt(0² + (-9)²)
= sqrt(0 + 81)
= sqrt(81)
= 9
Now let's determine the most specific name for this polygon. Since all sides have different lengths, we can conclude that this quadrilateral is not a special type of polygon like rectangle, square, or rhombus where the sides are equal. Based on the given information, the most specific name for this quadrilateral would simply be a "quadrilateral" since no additional properties have been mentioned to classify it further.