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Rus_ich [418]
3 years ago
5

The figure shows two triangles on a coordinate grid:

Mathematics
2 answers:
Afina-wow [57]3 years ago
3 0
IT IS CORRECT 5 UNIT DOWN TRANSLATION 180 DEGREE COUNTERCLOCKWISE ROTATION
Jobisdone [24]3 years ago
3 0

Answer: A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin .

Step-by-step explanation:

From the given figure, the coordinates of ΔABC are A(-3,4), B(-3,1), C(-2,1) and the coordinates of ΔA'B'C' are A'(3,1), B'(3,4), C'(2,4).

When, a translation of 5 units down is applied to  ΔABC, the coordinates of the image will be

(x,y)\rightarrow(x,y-5)\\A(-3,4)\rightarrow(-3,-1)\\ B(-3,1)\rightarrow(-3,-4)\\ C(-2,1)\rightarrow(-2,-4)

Then applying 180° counterclockwise rotation about the origin, the coordinates of the image will be :-

(x,y)\rightarrow(-x,-y)\\(-3,-1)\rightarrow(3,1)\\(-3,-4)\rightarrow(3,4)\\(-2,-4)\rightarrow(2,4) which are the coordinates of ΔA'B'C'.

Hence, the set of transformations is performed on triangle ABC to form triangle A’B’C’ is " A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin ".

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slope (m) = (y₂ - y₁)/(x₂ - x₁) = (0 - 3)/(15 - 0) = -3/15 = -1/5

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3 years ago
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Elena L [17]
<span><u><em>Answer:</em></u>
either y = 4.5
or y = -4.5

<u><em>Explanation:</em></u>
To get the solution, we will need to isolate the y on one side of the equation.
<u>This can be done as follows:</u>
4y</span>²<span> = 81

</span>\frac{4y^2}{4} =  \frac{81}{4}
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y</span>²<span> = 20.25

y = +/- </span>√(20.25)<span>
either y = +</span>√<span>(20.25) = 4.5
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Since there are no restrictions on the value of y, therefore, both answers would be accepted

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