Rhombus WXYZ has vertices W(1,2), X(4,3), Y(3,0) and Z(0,-1). Find the lengths of diagonals WY and XZ.
a.)WY=2√2; XZ=4√2
b.)WY=2√4; XZ=2√2
c.)WY=2√4; XZ=4√2
WY = √((3-1)^2 + (0-2)^2)
= √(4+4) = √8 = 2√2
XZ = √(4^2 + 4^2)
= √32 = 4√2
Thanks:)
To find the lengths of the diagonals WY and XZ in the rhombus WXYZ, we can use the distance formula.
The distance formula calculates the distance between two points (x1, y1) and (x2, y2) as follows:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For WY:
1. Identify the coordinates of the two points that make up the diagonal WY. In this case, it's W(1,2) and Y(3,0).
2. Apply the distance formula to find the length of WY:
Distance WY = √((3 - 1)^2 + (0 - 2)^2)
= √(2^2 + (-2)^2)
= √(4 + 4)
= √8
= 2√2
For XZ:
1. Identify the coordinates of the two points that make up the diagonal XZ. In this case, it's X(4,3) and Z(0,-1).
2. Apply the distance formula to find the length of XZ:
Distance XZ = √((0 - 4)^2 + (-1 - 3)^2)
= √((-4)^2 + (-4)^2)
= √(16 + 16)
= √32
= 4√2
Therefore, the correct answer is:
a.) WY = 2√2; XZ = 4√2