Question

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

Answer 1

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 ........

Answer 2

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.