The quadrilateral with the vertices C(-3,-5), R(5,1), U(2,3) and D(-2,0) is a Blank 1 Question 10

To determine the type of quadrilateral CRUD, we need to calculate the lengths of its sides and diagonals.

Step 1: Calculate the lengths of the sides Use the distance formula: √[(x₂ - x₁)² + (y₂ - y₁)²]

CR = √[(5 - (-3))² + (1 - (-5))²] = √[(8)² + (6)²] = √100 = 10 RU = √[(2 - 5)² + (3 - 1)²] = √[(-3)² + (2)²] = √13 UD = √[(-2 - 2)² + (0 - 3)²] = √[(-4)² + (-3)²] = √25 = 5 DC = √[(-3 - (-2))² + (-5 - 0)²] = √[(-1)² + (-5)²] = √26

Step 2: Calculate the lengths of the diagonals Use the distance formula: √[(x₂ - x₁)² + (y₂ - y₁)²]

CU = √[(2 - (-3))² + (3 - (-5))²] = √[(5)² + (8)²] = √89 RD = √[(5 - (-2))² + (1 - 0)²] = √[(7)² + (1)²] = √50

Step 3: Compare the lengths of the sides and diagonals We see that CR = UD and RU = DC, but the diagonals CU and RD are not equal.

Therefore, the quadrilateral CRUD is a parallelogram.