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.
square units
C.
30 square units
D.
square units
B. 15 square units
To find the area of triangle X-Y-Z, we can use the formula for the area of a triangle given by (1/2) * base * height. In this case, the base is the distance between points X and Z, which can be found using the distance formula:
d = √((x2-x1)^2 + (y2-y1)^2)
d = √((5-0)^2 + (3-8)^2) = √(25 + 25) = √50
Now, we need to find the height of the triangle. Since the line Y-P is perpendicular to line X-Z, we can see that the height is the y-coordinate of point Y, which is 8.
Now we can calculate the area of the triangle:
Area = (1/2) * base * height
Area = (1/2) * √50 * 8
Area = 4 * √50
Area ≈ 15 square units
Therefore, the correct answer is 15 square units.