Given:
Point A (-3.0,-5.4)
Point B (-3.0,5.4)
reflection across y-axis ⇒ (a,b) reflected (-a,b)
reflection across x-axis ⇒ (a,b) reflected (a,-b)
reflection across the origin ⇒ (a,b) reflected (-a,-b)
reflection on y = x ⇒ (a,b) reflected (b,a)
Point B is a reflection of Point A across the x-axis.
we have
Adds 
both sides
square root both sides
therefore
<u>the answer is</u>
the resulting equation is 
Each of these roots can be expressed as a binomial:
(x+1)=0, which solves to -1
(x-3)=0, which solves to 3
(x-3i)=0 which solves to 3i
(x+3i)=0, which solves to -3i
There are four roots, so our final equation will have x^4 as the least degree
Multiply them together. I'll multiply the i binomials first:
(x-3i)(x+3i) = x²+3ix-3ix-9i²
x²-9i²
x²+9 [since i²=-1]
Now I'll multiply the first two binomials together:
(x+1)(x-3) = x²-3x+x-3
x²-2x-3
Lastly, we'll multiply the two derived terms together:
(x²+9)(x²-2x-3) [from the binomial, I'll distribute the first term, then the second term, and I'll stack them so we can simply add like terms together]
x^4 -2x³-3x²
<u> +9x²-18x-27</u>
x^4-2x³+6x²-18x-27
Applying the coordinate rules for the output, the output for the given inputs are :
The rule :
(x, y)→(x−7.5, y+6.8)
- For the x - coordinate ; Subtract 7.5
- For the y - coordinate `; add 6.8
First input : (4.3, 5.5)
- Output :
- x = 4.3 - 7.5 = - 3.2
- y = 5.5 + 6.8 = 12.3
- Output = (4.3, 5.5) →(-3.2 , 12.3)
Second input : (8.2, -3.2)
- Output :
- x = 8.2 - 7.5 = 0.7
- y = - 3.2 + 6.8 = 3.6
- Output = (8.2, -3.2)→(0.7 , 3.6)
The outputs obtained are :
- (-3.2 , 12.3) and (0.7 , 3.6)
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