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LiRa [457]
3 years ago
7

Segment FG begins at point F(-2, 4) and ends at point G (-2, -3). Segment FG is translated by (x, y) → (x – 3, y + 2) and then r

eflected across the y-axis to form segment F'G'. How long is segment F'G'?
Mathematics
1 answer:
Mariana [72]3 years ago
8 0

Answer:

The length of the segment F'G' is 7.

Step-by-step explanation:

From Linear Algebra we define reflection across the y-axis as follows:

(x',y')=(-x, y), \forall\, x, y\in \mathbb{R} (Eq. 1)

In addition, we get this translation formula from the statement of the problem:

(x',y') =(x-3,y+2), \forall \,x,y\in \mathbb{R} (Eq. 2)

Where:

(x, y) - Original point, dimensionless.

(x', y') - Transformed point, dimensionless.

If we know that F(x,y) = (-2, 4) and G(x,y) = (-2,-3), then we proceed to make all needed operations:

Translation

F''(x,y) = (-2-3,4+2)

F''(x,y) = (-5,6)

G''(x,y) = (-2-3,-3+2)

G''(x,y) = (-5,-1)

Reflection

F'(x,y) = (5, 6)

G'(x,y) = (5,-1)

Lastly, we calculate the length of the segment F'G' by Pythagorean Theorem:

F'G' = \sqrt{(5-5)^{2}+[(-1)-6]^{2}}

F'G' = 7

The length of the segment F'G' is 7.

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Bas_tet [7]
Since congruence and similarity for polygons is posted in a specific order, we know that angle A=angle F, side A=side F, die B=side G, and so on. Therefore, we have that angle C=angle H = 9x-7=5x+13. Subtracting 5x from both sides to separate the x using the subtraction property of equality, we get 4x-7=13. Next, we can add 7 to both sides to get 4x=20, and divide both sides by 4 to isolate the x and get x=5. Plugging that into angle C or angle H, we get that 9x-7=9*5-7=45-7=38=5*5+13.

Feel free to ask further questions!
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3 years ago
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I interpreted the remainder by removing the remainder to get the answer.
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3 years ago
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9.01 maybe my math might be wrong

Step-by-step explanation:

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2 years ago
Mrs. Simpson is frosting circular sugar cookies. Each cookie is 7 cm in diameter. How many square inches will she need to frost
Alexus [3.1K]

Answer:

51.92 square inches

Step-by-step explanation:

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2 years ago
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