anonymous
  • anonymous
If a line is not horizontal or vertical, how is the slope of the line related to the slope of its reflection image in each of the following? a) x-axis and b) y-axis Please explain. D:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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campbell_st
  • campbell_st
the slope the reflection is the inverse of the slope of the original line. the point (3, 2) will become (2,3) x and y values are transposed.
anonymous
  • anonymous
ohh..
Mani_Jha
  • Mani_Jha
Just to add to campbell's answer, |dw:1332647836839:dw| The slope of the original line is \[m=\tan \theta\] The slope of the reflection through x-axis is: \[\tan(-\theta)=-\tan \theta=-m\] The slope of the reflection through y-axis is: \[\tan(90+\theta)=-\cot \theta=-1/m\] Clear?

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anonymous
  • anonymous
how is the slope of a line tan \[\theta\]
Mani_Jha
  • Mani_Jha
That's the definition of slope. It is the tangent of the angle that the line it makes with the positive x-axis. Do you want to know why, through the proof?
anonymous
  • anonymous
yes please :$
Callisto
  • Callisto
For it reflecting along y-axis
1 Attachment
Mani_Jha
  • Mani_Jha
Oh yes. The angle should be (180-theta) not (90+theta). Sorry for that!
anonymous
  • anonymous
oh, it's okay!
Callisto
  • Callisto
For it reflecting along x-axis
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anonymous
  • anonymous
oouu, thank you!
Callisto
  • Callisto
So.. maybe for it reflecting along x-axis/y-axis, the new slope also becomes -ve of the original slope.
Callisto
  • Callisto
BTW, do you understand?
anonymous
  • anonymous
yup I sort of but I don't get the -ve?
Mani_Jha
  • Mani_Jha
The word 'slope' means incilination or slant. It can be measured by the ratio of 'rise' to the horizontal distance. |dw:1332648809596:dw| Let's consider any 2 points (x1,y1) and (x2,y2). We shall measure how much rise and how much horizontal distance has been covered from (x1,y1) to (x2,y2) Rise=y2-y1 Horizontal distance=x2-x1 Slope=(y2-y1)/(x2-x1) See that in the triangle in the top part, this ratio is equal to tan(theta). Get it?
Callisto
  • Callisto
-ve = negative...
anonymous
  • anonymous
ohhhhh, i get it (sort of but I'm getting it) thank you guys!
Callisto
  • Callisto
you're welcome!

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