Reflection in terms of coordinates refers to the transformation of a point or object on a coordinate grid across a line of reflection. This creates a mirror image of the original point or object on the other side of the line.
To determine the line of reflection given an equation, you first need to find the slope of the line. This can be done by rearranging the equation to the form y = mx + b, where m is the slope. The line of reflection will be perpendicular to this line and will have the same y-intercept.
The formula for finding the coordinates of reflection is (x,y) --> (x,-y) or (x,y) --> (-x,y), depending on whether the line of reflection is the x-axis or the y-axis, respectively. This means that the x-coordinate stays the same, while the y-coordinate is multiplied by -1.
Yes, for example, if the original point is (3,5) and the line of reflection is the x-axis, the reflected point would be (3,-5). If the line of reflection is the y-axis, the reflected point would be (-3,5).
You can check if the coordinates of reflection are correct by graphing the original point and the reflected point on a coordinate grid and verifying that they are symmetric across the line of reflection. You can also substitute the reflected point into the original equation and see if it satisfies the equation.