The figure below shows graphed on the coordinate plane.
Triangle X-Y-Z with a perpendicular line P-Y from vertex Y on line X-Z forming two right triangles X-Y-P and Z-Y-P. Triangle X-Y-Z has its vertices X at (0, 8), Y at (6, 8) and Z at (5, 3).
What is the area of ?
A.
15 square units
B.
15√2 square units
C.
30 square units
D.
30√2 square units
First, we need to find the length of line segment X-Z and line segment Y-P.
Using the distance formula, the length of line segment X-Z is:
√((5-0)^2 + (3-8)^2) = √(25 + 25) = √50 = 5√2
The length of line segment Y-P can be found by subtracting the x-coordinates of Y and P:
6 - 5 = 1
Now, we can find the area of triangle X-Y-Z:
Area = (1/2) * base * height
Area = (1/2) * 5√2 * 5
Area = 12.5√2 square units
Therefore, the correct answer is:
B. 15√2 square units