Answer:
square
Step-by-step explanation:
Here are the steps to determine the quadrilateral's type:
1. Calculate side lengths using the distance
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Where
- (x₁, y₁) are the coordinates of the first point.
- (x₂, y₂) are the coordinates of the second point.
AB = √((2-1)^2 + (3-5)^2) = √5
BD = √((2-0)^2 + (3-2)^2) = √5
CD = √((-1-0)^2 + (4-2)^2) = √5
AC = √((-1-1)^2 + (4-5)^2) = √5
2. Check for parallel sides using slopes:
Slope (m) = (y₂ - y₁) / (x₂ - x₁)
- (x₁, y₁) are the coordinates of the first point.
- (x₂, y₂) are the coordinates of the second point.
Slope of AB = (5-3)/(1-2) = -2
Slope of CD = (4-2)/(-1-0) = -2
AB and CD have the same slope, so they are parallel.
Slope of BD = (3-2)/(2-0) = 1/2
Slope of AC = (5-4)/(1-(-1)) = 1/2
BD and AC have the same slope, so they are parallel.
3. Check for right angles using perpendicular slopes:
The product of slopes of perpendicular lines is -1.
The slope of the AB Slope of BD = -2 1/2 = -1, so AB is perpendicular to BD.
The slope of the AB Slope of AC = -2 1/2 = -1, so AB is perpendicular to AC.
4. Determine the quadrilateral's type:
Since all sides are equal (√5), opposite sides are parallel, and adjacent sides are perpendicular, the quadrilateral is a square.
Therefore, the quadrilateral ABDC is a square.
