Asked by Anonymous
The point (2.2) is reflected in the line y = -0.5x + 2. Determine the coordinates of the mirror image.
what does mirror image mean? the opposite on the other side? how would that work in this case
thankyou
what does mirror image mean? the opposite on the other side? how would that work in this case
thankyou
Answers
Answered by
Reiny
Make sketch of the line y = (-1/2)x + 2, and plot the point A(2,2)
notice that (2,2) does not lie on the line, it is above it
The image of the reflection A would be a point B(a,b) so that AB
has the given line as its right-bisector.
How about we find the equation of AB, we know its slope is +2 and it passes
through (2,2)
y = 2x + b, at (2,2) ---> 2 = 4 + b
b = -2
equation of AB is y = 2x -2
it meets the given line when 2x - 2 = (-1/2)x + 2
4x - 4 = -x + 4
5x = 8
x = 8/5 , then y = 16/5 - 2 = 6/5
Clearly, (8/5 , 6/5) must be the midpoint of AB, that is
(a+2)/2 = 8/5 and (b+2)/2 = 6/5
a+2 = 16/5 and b+2 = 12/5
a = 6/5 and b = 2/5
so the image of (2,2) after a reflection in y = (-1/2)x + 2 is ........
notice that (2,2) does not lie on the line, it is above it
The image of the reflection A would be a point B(a,b) so that AB
has the given line as its right-bisector.
How about we find the equation of AB, we know its slope is +2 and it passes
through (2,2)
y = 2x + b, at (2,2) ---> 2 = 4 + b
b = -2
equation of AB is y = 2x -2
it meets the given line when 2x - 2 = (-1/2)x + 2
4x - 4 = -x + 4
5x = 8
x = 8/5 , then y = 16/5 - 2 = 6/5
Clearly, (8/5 , 6/5) must be the midpoint of AB, that is
(a+2)/2 = 8/5 and (b+2)/2 = 6/5
a+2 = 16/5 and b+2 = 12/5
a = 6/5 and b = 2/5
so the image of (2,2) after a reflection in y = (-1/2)x + 2 is ........
Answered by
oobleck
the opposite on the other side
you want to find a point the same distance on the other side of the line. It must also lie on a line perpendicular to your given line.
google can provide you with many discussions and examples of reflection through any line.
you want to find a point the same distance on the other side of the line. It must also lie on a line perpendicular to your given line.
google can provide you with many discussions and examples of reflection through any line.
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