(5,2),(3,-5),(-5,-1) find the area of triangle ?

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(5,2),(3,-5),(-5,-1) find the area of triangle ?

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Answer 1 · 2018-04-24T06:17:27

$A = 32$ $A = 32$ Square Units

Explanation:

Let: $A (5, 2)$ $A(5,2)$ , $B (3, - 5)$ $B(3, -5)$ , $C (- 5, - 1)$ $C(-5, -1)$ , then:

Shift $C$ $C$ to Origin $(0, 0)$ $(0, 0)$ , and also:

Adjust $A$ $A$ and $B$ $B$ to compensate for the shift accordingly:

$C (- 5 + 5, - 1 + 1) \Rightarrow C (0, 0)$ $C(-5+5 , -1+1) => C(0, 0)$
$A (5 + 5, 2 + 1) \Rightarrow A (10, 3)$ $A(5+5, 2+1) => A(10, 3)$
$B (3 + 5, - 5 + 1) \Rightarrow C (8, - 4)$ $B(3+5, -5+1) => C(8, -4)$

Then we can use the following:

Area of the triangle with vertices at:

$C (0, 0)$ $C(0, 0)$ , $A (x_{1}, y_{1})$ $A(x_1, y_1)$ , and $B (x_{2}, y_{2})$ $B(x_2, y_2)$ is:

Area = $\frac{1}{2} | x_{1} y_{2} - x_{2} y_{1} |$ $1/2|x_1 y_2 - x_2 y_1|$

Therefore in this case we get:

$A = \frac{1}{2} | (10) (- 4) - (8) (3) |$ $A=1/2|(10)(-4)-(8)(3)|$

$A = \frac{1}{2} | - 40 - 24 |$ $A= 1/2|-40-24|$

$A = \frac{1}{2} | - 64 |$ $A=1/2|-64|$

$A = \frac{1}{2} \cdot 64$ $A= 1/2*64$

$A = 32$ $A = 32$ Square Units

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(5,2),(3,-5),(-5,-1) find the area of triangle ?

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