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Y_Kistochka [10]
3 years ago
9

Graph ΔABC and its image after a rotation of 180º about the origin.

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
3 0

Answer:

The vertices of image are A'(0,0), B'(-1,-5) and C'(4,-5). The graph of image and preimage is shown below.

Step-by-step explanation:

From the given figure it is noticed that the vertices of  triangle ABC are A(0,0), B(1,5) and C(-4,5).

If a figure rotated at 180º about the origin, then

P(x,y)\rightarrow P'(-x,-y)

The vertices of image are

A(0,0)\rightarrow A'(0,0)

B(1,5)\rightarrow B'(-1,-5)

C(-4,5)\rightarrow C'(4,-5)

Therefore the vertices of image are A'(0,0), B'(-1,-5) and C'(4,-5).

The graph of image and preimage is shown below.

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Alinara [238K]

Answer:

\boxed {\boxed {\sf m \angle G = 63}}

Step-by-step explanation:

The angles in a triangle add to 180 degrees.

We are given triangle EFG. There are 3 angles: m∡E = 5x+6, m∡F = 4x-6, and m∡G = 5x-2.

The sum of these three angles must equal 180. Set up an equation and solve for x.

(5x+6)+(4x-6)+(5x-2)= 180

Combine like terms on the left side.

(5x+4x+5x) +  (6  + -6 -2) = 180

14x -2 = 180

Solve for x. 2 is being subtracted from 14x. The inverse operation of subtraction is addition. Add 2 to both sides.

14x-2+2=180+2 \\14x=182

x is being multiplied by 14. The inverse operation of multiplication is division. Divide both sides by 14.

\frac {14x}{14} = \frac{182}{14}

x= \frac{182}{14}

x=13

Find the measure of angle G. Substitute x into the original expression.

m \angle G =5x-2

m \angle G = 5 (13)-2\\m\angle G = 65-2 \\m\angle G = 63

The measure of angle G is 63 degrees.

5 0
2 years ago
Write a paragraph to describe the process of factoring the following expression.<br> x2 + 6x + 8
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Answer:

Step-by-step explanation:

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What is the measure of angle 2
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And since the triangles are congruent, angle 2 must be 69 degrees as well.

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3 years ago
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Answer:

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