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3 years ago

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.

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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.

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Answer:

Step-by-step explanation:

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