Use a determinant and the given vertices of a triangle to find the area of the triangle.? ?
A) $\frac { 2 } { 13 }$
B) $\frac { 6 } { 19 }$
C)18
D)38
E)40

Question

Use a determinant and the given vertices of a triangle to find the area of the triangle.?  ?
A) $\frac { 2 } { 13 }$ 
B) $\frac { 6 } { 19 }$ 
C)18 
D)38 
E)40

Quizplus · Accepted Answer

Using the determinant method, we can find the area of the triangle using the following formula:
Area = 1/2 * |(x1-x3)(y2-y3)-(x2-x3)(y1-y3)|
Substituting the given coordinates, we get:
Area = 1/2 * |(2-(-1))(4-(-1))-(6-(-1))(2-(-1))|
Area = 1/2 * |(3)(5)-(7)(3)|
Area = 1/2 * |-6| = 3
Therefore, the area of the triangle is 3*6=18. Hence, the best choice is C.

Use a Determinant and the Given Vertices of a Triangle 213\frac { 2 } { 13 }132​

Use a Determinant and the Given Vertices of a Triangle $\frac { 2 } { 13 }$