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lesya692 [45]
4 years ago
15

A reflection is a transformation that maps point A in a figure over a line, XY←→ , such that for point P at the intersection of

XY←→ and AA′¯¯¯¯¯¯ , ____ and ____.

Mathematics
1 answer:
harina [27]4 years ago
6 0

Answer:

  • point P is a midpoint of segment AA'
  • XY is perpendicular to AA'

Step-by-step explanation:

Consider given line XY and point A (see attached diagram for details).

To reflect point A over a line XY, you have to draw perpendicular line to the line XY passing through tha point A. This line intersects XT at point P. Then plot point A' such that A' lies on the line AP and AP=PA'.

Therefore,

  • point P is a midpoint of segment AA'
  • XY is perpendicular to AA'

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5 0
3 years ago
Find all solutions to the equation (x² + 5x + 6)(x² − 3x − 4) = 0.
Soloha48 [4]

Answer:

The solutions are:

x=-2,\:x=-3,\:x=-1,\:x=4

Step-by-step explanation:

To find the solutions to the equation \left(x^2+5x+6\right)\left(x^2-3x-4\right)=0 you need to:

  • Factor \left(x^2+5x+6\right)

Break the expression into groups

x^2+5x+6=\left(x^2+2x\right)+\left(3x+6\right)

Factor out x from (x^2+2x)

x^2+2x=x\left(x+2\right)

Factor out 3 from 3x+6

3x+6=3\left(x+2\right)

x^2+5x+6=x\left(x+2\right)+3\left(x+2\right)\\\\\mathrm{Factor\:out\:common\:term\:}x+2\\\\x^2+5x+6=\left(x+2\right)\left(x+3\right)

  • Factor \left(x^2-3x-4\right)

x^2-3x-4=\left(x^2+x\right)+\left(-4x-4\right)\\\\x^2-3x-4=x\left(x+1\right)-4\left(x+1\right)\\\\x^2-3x-4=\left(x+1\right)\left(x-4\right)

Therefore

\left(x^2+5x+6\right)\left(x^2-3x-4\right)=\left(x+2\right)\left(x+3\right)\left(x+1\right)\left(x-4\right)=0

Using the Zero Factor Theorem:

5 0
4 years ago
find the measure of the angle of the radius of the circle is 4 inches and the length of the arc is 8 pi.
NeTakaya
Since the angle is in radians, then s = rθ.

\bf \textit{arc's length}\\\\&#10;s=r\theta \quad &#10;\begin{cases}&#10;r=4\\&#10;s=8\pi &#10;\end{cases}\implies 8\pi =4\theta \implies \cfrac{8\pi }{4}=\theta \implies 2\pi =\theta
4 0
3 years ago
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