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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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bogdanovich [222]
5 * 198 = 990


 198
*    5
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6 0
3 years ago
Help on this please show my work ?
Mandarinka [93]
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3 years ago
Consider the polynomial f(x)=2x^5-3x^4+x-6 (x )equals 2 x Superscript 5 Baseline minus 3 x Superscript 4 Baseline plus x minus 6
melamori03 [73]

Answer:

degree of polynomial = 5

leading term = 2x^{5}

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constant term = -6

Step-by-step explanation:

f(x) = 2x^{5}-3x^{4}+x-6

(i) The degree of the polynomial = 5. That is, the highest power of x

(ii) Leading term = 2x^{5}. This is the term with the highest power of x.

(iii) Leading Coefficient = 2. That is, the coefficient of the leading term (2x^{5})

(iv) Constant term = -6. This is the term that is independent of x or the term in which x doesn't appear.

3 0
3 years ago
What is the slope of the line threw (-9,6) and (-3, 9)
DerKrebs [107]

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Answer: 1/2

4 0
3 years ago
Read 2 more answers
Whats is the answer to this question below?
uysha [10]

Hey there. So first we need to know what the point slope form looks like.

It is Y-Y1=M (X-X1)

Knowing this you just plug in the given information.

M is equal to 1/6. So in this case all of the options have the correct m. Next we look at the Year value. We know Y is a positive 4. So the beginning of the equation is going to look like

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Nown plug in x. It would be a negative 5. Now your final answer would be option A. Hope the explanation helped.. :)

4 0
3 years ago
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