![]() So the image (that is, point B) is the point (1/25, 232/25). For each of the figures points: - multiply the x-value by -1. 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. To sketch the graph of y loga x, you can use the fact that the graphs of inverse functions are reflections of each other in the line y x. 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). Put the coordinates into the equations of the reflecting line to see if theyre. ![]() So we first find the equation of the line through (2,9) that is perpendicular to the line y = 7x + 2. Explore math with our beautiful, free online graphing calculator. 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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