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Grade: 11

                        

the equation of the image of a pairof rays y=|x| by the line x=1 is makethe answer more elaborate

2 years ago

Answers : (1)

Susmita
425 Points
							
Follow the steps.
Draw x axis and y axis.
y=|x| is a straight line passing through origin.
y=x and y=-x will be symmetrically places about y axis.Draw them.They will look like a V (\|/) about the y axis.
x=1 is a line parallel to y axis and passing through the point (1,0). Draw it.This is the mirror.Now we have to make a mirror image of the V about it.
It will look like V|V.
x=1 will cut y=x at a point (1,1).
See that the perpedicular distance(or distance from origin to x=1) of y=x from x=1(mirror) is 1.So the image of y=x will also cut the x axis 1 unit away  from x=1(mirror) on the right side of the mirror or (1+1)=2 unit from the origin on the x axis.
That means the image of y=x passes through two points (1,1) and (2,0).Equation of this line is 
(x-1)/(2-1)=(y-1)/(0-1)
Or,x-1=-y+1
Or,y=-(x-2)
Proceeding like this for the line y=-x,you will find image of it is
y=(x-2)
So taking mode equation of image is
y=|x-2|
 
2 years ago
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