△ABC has verticles A(1,1), B(1,7), and C(6,5).
What is the area of △ABC?
A. 12 units
B. 15 units
C. 20 units
D. 14 units
If you let AB be the base, then it is easy to see that the altitude is 5.
1/2 (6)(5) = 15
A = 1/2(h*b) = 1/2(7-1)(6-1) = 15 units.
To find the area of triangle ABC, we can use the formula for the area of a triangle given the coordinates of its vertices.
The formula for the area of a triangle with coordinates A(x1, y1), B(x2, y2), and C(x3, y3) is:
Area = |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)) / 2|
In this case, A(1,1), B(1,7), and C(6,5).
Substituting these values into the formula, we get:
Area = |(1(7 - 5) + 1(5 - 1) + 6(1 - 7)) / 2|
Simplifying the expression inside the absolute value, we get:
Area = |(2 + 4 - 36) / 2|
Calculating further, we get:
Area = |-30 / 2|
Area = 15
Therefore, the area of triangle ABC is 15 square units.
The correct answer is B. 15 units.