Use a determinant and the given vertices of a triangle to find the area of the triangle.? ?
A)52
B) $\frac { 4 } { 19 }$
C)25
D) $\frac { 2 } { 17 }$
E)54

Question

Use a determinant and the given vertices of a triangle to find the area of the triangle.?  ?
A)52 
B) $\frac { 4 } { 19 }$ 
C)25 
D) $\frac { 2 } { 17 }$ 
E)54

Quizplus · Accepted Answer

To find the area of a triangle using determinants, we use the formula:

Area = 1/2 |x1  y1  1|
                    |x2  y2  1|
                    |x3  y3  1|

where (x1, y1), (x2, y2), and (x3, y3) are the vertices of the triangle.

Plugging in the values from the given vertices, we get:

Area = 1/2 |4   1   1|
                     |2   7   1|
                     |-1  3   1|

Using a calculator or by hand, we can evaluate this determinant to find that the area is 25. Therefore, the correct answer is (C).

Use a Determinant and the Given Vertices of a Triangle 419\frac { 4 } { 19 }194​

Use a Determinant and the Given Vertices of a Triangle $\frac { 4 } { 19 }$