Y=6x-8 solve in system of equations using the method substitution

A reflection is a type of transformation uses a line that acts like a mirror, with an image reflected in the line. The mirror line is the line of reflection. A transformation is an isometry, which preserves lengths, angle measures, parallel lines, and distances between points.

A reflection in the line m is a transformation that maps every point P in the plane to a point P′ such that the following properties are true:

If P is not on m, then m is the perpendicular bisector of . This means that it divides into two congruent parts at a right angle.

If P is on m, then P = P′.

Reflections in Coordinate Plane

The line of reflection acts like a mirror between the preimage and its image.

Reflections in the coordinate axes can be found by applying the following rules:

1. If (x, y) is reflected in the x-axis, its image is the point (x, -y). The y-coordinate is negated when reflecting in the x-axis. The rule is (x, y) → (x, -y).
2. If (x, y) is reflected in the y-axis, its image is the point (-x, y). The x-coordinate is negated when reflecting in the y-axis. The rule is (x, y) → (-x, y).
3. If (x, y) is reflected in the line y = x, its image is (y, x). The line y = x is a line with a slope of 1 and a y-intercept of 0. The x-coordinate and the y-coordinate are switched when reflecting in the line y = x. The rule is (x, y) → (y, x).

For example, consider the point (4, 1).
Reflected in the x-axis: the rule is (x, y) → (x, -y), (4, 1) → (4, -1).
Reflected in the y-axis: the rule is (x, y) → (-x, y), (4, 1) → (-4, 1).
Reflected in the line y = x-axis: the rule is (x, y) → (y, x), (4, 1) → (1, 4).