The figure below shows graphed on the coordinate plane.
X= (0,8)
Y= (6,8)
Z= (5,3)
What is the area of XYZ?
A.
15 square units
B.
15√2 square units
C.
30 square units
D.
30√2 square units
To find the area of XYZ, we can use the shoelace formula. This formula states that the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by:
Area = |(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3)/2|
Using the given points X = (0,8), Y = (6,8), and Z = (5,3), we can substitute the coordinates into the shoelace formula:
Area = |(0*8 + 6*3 + 5*8 - 6*8 - 5*3 - 0*3)/2|
= |(0 + 18 + 40 - 48 - 15 - 0)/2|
= |(0)/2|
= 0
Therefore, the area of XYZ is 0 square units. None of the given options match this answer.