![]() So the image (that is, point B) is the point (1/25, 232/25). 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. In the end, we found out that after a reflection over the line x-3, the coordinate points of the image are: A(0,1), B(-1,5), and C(-1, 2) Vertical Reflection. Substituting the point (2,9) givesĩ = (-1/7)(2) + b which gives b = 65/7. The y-value will not be changing, so the coordinate point for point A’ would be (0, 1) Repeat for points B and C. So the desired line has an equation of the form y = (-1/7)x + b. In math, you can create mirror images of figures by reflecting them over a given line. 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). When you look in the mirror, you see your reflection. 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. In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates. 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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