use the determinant method to find the area of a

Ответ:

Tobymorgan3287

16.03.2022

Mathematics

Area of triangle is 12.5

Step-by-step explanation:

We need to use the determinant method to find the area of a triangle ABC with vertices at A (1,6) B (4,2) and C (-3,3)

The formula used is: $Area=\pm \frac{1}{2}\left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{array}\right|$

We are given:

x_1=1,y_1=6,x_2=4,y_2=2,x_3=-3,y_3=3

Putting values and finding area

$Area=\frac{1}{2}\left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{array}\right|\\Area=\frac{1}{2}\left|\begin{array}{ccc}1&6&1\\4&2&1\\-3&3&1\end{array}\right|\\Area=\frac{1}{2}(1\left|\begin{array}{cc}2&1\\3&1\end{array}\right|-6\left|\begin{array}{cc}4&1\\-3&1\end{array}\right|+1\left|\begin{array}{cc}4&2\\-3&3\end{array}\right| )\\Area=\frac{1}{2}(1(2-3)-6(4-(-3))+1(12-(-6)))\\Area= \frac{1}{2}(1(-1)-6(4+3)+1(12+6))\\Area= \frac{1}{2}(1(-1)-6(7)+1(18))\\Area= \frac{1}{2}(-1-42+18)\\$

$Area=\frac{1}{2}(-25)\\Area=-12.5\\$

We take mode of -12.5 i.e. |-12.5| because area can't be negative.

$Now, \\Area=|-12.5|\\Area=12.5$

So, Area of triangle is 12.5

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Ответ:

firefightergros3547

03.07.2022

Mathematics

In general, the students increased their standardized math scores from 5th grade to 7th grade. The students might be more familiar with the exam and they have learned more in their math classes.

Step-by-step explanation:

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use the determinant method to find the area of a triangle ABC with vertices at A (1,6) B (4,2) and C (-3,3)

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