1. What is the most precise classification of the quadrilateral? Hint: (use distance formula, slopes of sides, etc to support answer) Q(4, 5), U(12, 14), A(20, 5), D(12, - 4)
Answer is rhombus but how would I show my work
To show that this quadrilateral is a rhombus, we can use the distance formula to calculate the lengths of the sides.
The length of side QU is √((12-4)^2 + (14-5)^2) = √(64 + 81) = √145
The length of side UA is √((20-12)^2 + (5-14)^2) = √(64 + 81) = √145
The length of side AD is √((12-20)^2 + (-4-5)^2) = √(64 + 81) = √145
The length of side QD is √((4-12)^2 + (5-(-4))^2) = √(64 + 81) = √145
Since all four sides have the same length, this quadrilateral is a rhombus.