So, if we were to reflect (4, 3) over the y-axis, we would get (4, -3). Similarly, to reflect a point or line over the y-axis, we would take the y-coordinate and change its sign to negative. So, the reflection of (4, 3) over the x-axis would be (-4, 3). The y-coordinate would remain unchanged (3 –> 3). To reflect this point over the x-axis, we would take the x-coordinate (4) and change its sign to negative (4 –> -4). Once the axis of reflection has been identified, all points and lines on one side of the axis must be reflected over to the other side.įor example, consider the point (4, 3). ![]() The x-axis is a horizontal line that runs from left to right, while the y-axis is a vertical line that runs from top to bottom. ![]() When reflecting points and lines in the coordinate plane, it is important to first identify the axis of reflection. How to Reflect Points and Lines in the Coordinate Plane Again, this results in a mirror image of the original. Similarly, when we reflect an image over the y-axis, we are flipping the image across a line that runs vertically through its center. This results in a mirror image of the original. When we reflect an image over the x-axis, we are essentially flipping the image across a line that runs horizontally through its center. For example, if a point had coordinates (3, 4), its new coordinates would be (3, -4). This means that all of the points in the figure will have coordinates that are opposites of their original coordinates. When we reflect a figure over the x-axis, we are essentially flipping the figure over a line parallel to the y-axis. In three dimensions, it can be used to find the equation of a plane given three points on that plane, or to find the points of intersection of a plane and a line. In two dimensions, it can be used to find the equation of a line given two points on that line, or to find the points of intersection of two lines. In mathematics, the rule of reflections is a method of solving certain types of problems by reflection. Reflections over the y-axis are called horizontal reflections. ![]() Reflections over the x-axis are called vertical reflections. There are two types of reflections: reflections over the x-axis and reflections over the y-axis. The point where the figure meets the axis of reflection is called the line of reflection. The line is called the axis of reflection. A reflection is a transformation that flips a figure over a line. In mathematics, reflections are a type of transformation. So the image (that is, point B) is the point (1/25, 232/25).Reflection Over X Axis and Y Axis Introduction So the intersection of the two lines is the point C(51/50, 457/50). ![]() Now we need to find the intersection of the lines y = 7x + 2 and y = (-1/7)x + 65/7 by solving this system of equations. So the equation of this line is y = (-1/7)x + 65/7. So the desired line has an equation of the form y = (-1/7)x + b. Since the line y = 7x + 2 has slope 7, the desired line (that is, line AB) has slope -1/7 as well as passing through (2,9). So we first find the equation of the line through (2,9) that is perpendicular to the line y = 7x + 2. Then, using the fact that C is the midpoint of segment AB, we can finally determine point B.Įxample: suppose we want to reflect the point A(2,9) about the line k with equation y = 7x + 2. Then we can algebraically find point C, which is the intersection of these two lines. So we can first find the equation of the line through point A that is perpendicular to line k. Note that line AB must be perpendicular to line k, and C must be the midpoint of segment AB (from the definition of a reflection). Let A be the point to be reflected, let k be the line about which the point is reflected, let B represent the desired point (image), and let C represent the intersection of line k and line AB.
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