Mathematics: Given ΔBUG as shown with B(-3,-1), U(-3,3) and G(4,1). Find the area of triangle BUG.

Given ΔBUG as shown with B(-3,-1), U(-3,3) and G(4,1).

Ответ:

Jasten

23.01.2022

Using symmetric expression, the area of triangle BUG is: 14 sq. units.

Recall:

The area of a triangle with coordinates of the vertices given can be calculated using the symmetric expression given as: $Area = \frac{1}{2} [x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)]$ Let,

$B(-3,-1) = (x_1, y_1)\\\\U(-3,3) = (x_2, y_2)\\\\G(4,1) = (x_3, y_3)$

Plug in the values into $Area = \frac{1}{2} [x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)]$

$Area = \frac{1}{2} [-3(3 - 1) + (-3)(1 - (-1)) + 4(-1 - 3)]\\\\Area = \frac{1}{2} [-3(2) + (-3)(2) + 4(-4)]\\\\Area = \frac{1}{2} [-6 + (-6) + (-16)}\\\\Area = \frac{1}{2} [-6 - 6 -16]\\\\Area = \frac{1}{2} [-28]\\\\\mathbf{Area = 14 sq. units}$

Therefore, using symmetric expression, the area of triangle BUG is: 14 sq. units.

Learn more about area of triangle on:

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Ответ:

magicalpenguin48

23.01.2022

Mathematics

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,

$A=\frac{1}{2} [x_{1} (y_{2} - y_{3} ) + x_{2} ( y_{3} - y_{1} )+x_{3} (y_{1} - y_{2} )]$ ..............(1)

Where, $(x_{1} ,y_{1} )$ , $(x_{2} ,y_{2} )$ and $(x_{3} ,y_{3} )$ are the coordinates of triangle

From the given values,

B ( -3, -1 ) = $(x_{1} ,y_{1} )$

U ( - 3, 3 ) = $(x_{2} ,y_{2} )$

G ( 4 , 1 ) = $(x_{3} ,y_{3} )$

Equation (1) becomes,

$A=\frac{1}{2} [ -3(3-1)+(3)(1-(-1))+4(-1-3)]$

$=\frac{1}{2} [ -3(2)+(3)(1+1)+4(-4)]$

$=\frac{1}{2} [ -6 -6 - 16 ]$

$=\frac{1}{2} [ -28 ]$

= - 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).

Given ΔBUG as shown with B(-3,-1), U(-3,3) and G(4,1). Find the area of triangle BUG.

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Ответ:

jessica6597

25.07.2022

Mathematics

Step-by-step explanation:

The complete question is

Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool?

A coordinate plane with quadrilateral ABCD at A 0 comma 2, B 3 comma 5, C 7 comma 1, and D 4 comma negative 2. Angles A and C are right angles, the length of segment AB is 4 and 24 hundredths units, and the length of diagonal BD is 7 and 7 hundredths units

we have

The coordinates of the pool are

A(0,2),B(3,5),C(7,1),D(4,-2)

Applying the Pythagoras Theorem

Find out the length of side AD

substitute the given values

Find the perimeter of the pool

The perimeter of a quadrilateral is equal to

substitute

see the attached figure to better understand the problem

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Given ΔBUG as shown with B(-3,-1), U(-3,3) and G(4,1). Find the area of triangle BUG.

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