. Find the area of a triangle ABC with vertices
A(2, 3), B(4, 7) and C(7, 3)
A. 20 1
2
π’πππ‘π 2.
B. β10 π’πππ‘π 2
C. 10 1
2
π’πππ‘π 2
D. 10 π’πππ‘π 2
We can use the formula for the area of a triangle given its vertices in the coordinate plane:
Area = 1/2 |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))|
Substituting the x and y coordinates of the given vertices, we get:
Area = 1/2 |(2(7-3) + 4(3-3) + 7(3-7))|
Simplifying, we get:
Area = 1/2 |(8-16)|
Area = 1/2 |-8|
Area = 4
Therefore, the area of triangle ABC is 4 square units, which is not one of the multiple choice options given. So there might be a typo in the question or the answer choices.
To find the area of triangle ABC, you can use the formula for the area of a triangle given its vertices:
Area = 1/2 * |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))|
where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the vertices A, B, and C, respectively.
Let's plug in the coordinates:
Area = 1/2 * |(2(7-3) + 4(3-7) + 7(4-3))|
= 1/2 * |(2(4) + 4(-4) + 7(1))|
= 1/2 * |(8 - 16 + 7)|
= 1/2 * |-1|
= 1/2 * 1
= 1/2
So, the area of triangle ABC is 1/2 square units.
Therefore, the correct answer is A. 1/2 square units.