The area of triangle BUG is 14 square units, it is obtained from the points of B(-3,-1), U(-3,3) and G(4,1).
Step-by-step explanation:
The given is,
B(-3,-1), U(-3,3) and G(4,1)
Step:1
Formula for area of triangle with coordinates,
[tex]A=\frac{1}{2} [x_{1} (y_{2} - y_{3} ) + x_{2} ( y_{3} - y_{1} )+x_{3} (y_{1} - y_{2} )][/tex]..............(1)
Where, [tex](x_{1} ,y_{1} )[/tex], [tex](x_{2} ,y_{2} )[/tex] and [tex](x_{3} ,y_{3} )[/tex] are the coordinates of triangle
From the given values,
B ( -3, -1 ) = [tex](x_{1} ,y_{1} )[/tex]
U ( - 3, 3 ) = [tex](x_{2} ,y_{2} )[/tex]
G ( 4 , 1 ) = [tex](x_{3} ,y_{3} )[/tex]
Equation (1) becomes,
[tex]A=\frac{1}{2} [ -3(3-1)+(3)(1-(-1))+4(-1-3)][/tex]
[tex]=\frac{1}{2} [ -3(2)+(3)(1+1)+4(-4)][/tex]
[tex]=\frac{1}{2} [ -6 -6 - 16 ][/tex]
[tex]=\frac{1}{2} [ -28 ][/tex]
= - 14 (Negative sign indicates clockwise traversal)
A = 14 square units
Result:
The area of triangle BUG is 14 square units, it is obtained from the points of B(-3,-1), U(-3,3) and G(4,1).
Using symmetric expression, the area of triangle BUG is: 14 sq. units.
Recall:
[tex]B(-3,-1) = (x_1, y_1)\\\\U(-3,3) = (x_2, y_2)\\\\G(4,1) = (x_3, y_3)[/tex]
[tex]Area = \frac{1}{2} [-3(3 - 1) + (-3)(1 - (-1)) + 4(-1 - 3)]\\\\Area = \frac{1}{2} [-3(2) + (-3)(2) + 4(-4)]\\\\Area = \frac{1}{2} [-6 + (-6) + (-16)}\\\\Area = \frac{1}{2} [-6 - 6 -16]\\\\Area = \frac{1}{2} [-28]\\\\\mathbf{Area = 14 sq. units}[/tex]
Therefore, using symmetric expression, the area of triangle BUG is: 14 sq. units.
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