![]() So the image (that is, point B) is the point (1/25, 232/25). There are four types of transformations: reflections, rotations. Recall that A is the point (2,9).ī = C + (C - A) = (51/50 + 51/50 - 2, 457/50 + 457/50 - 9) = (1/25, 232/25). A transformation takes a figure and manipulates it by moving it in the coordinate plane. So the intersection of the two lines is the point C(51/50, 457/50). The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the -value the same. ![]() You dont have to graph a point to find its reflection point. Just memorize these formulas and youll be good. To reflect across the line y-x, use the rule (-y, -x). By examining the coordinates of the reflected image, you can determine the line of reflection. 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. To reflect across the line yx, use the rule (y, x). A reflection is an example of a transformation that takes a shape (called the preimage) and flips it across a line (called the line of reflection) to create a new shape (called the image). So the equation of this line is y = (-1/7)x + 65/7. What to do to reflect ordered pairs across the x-axis, the. So the desired line has an equation of the form y = (-1/7)x + b. 1.8K views 4 years ago High School Geometry Course An explanation of the rules we would use for Reflections in the coordinate plane. An image will reflect through a line, known as the line of reflection. By studying what happens to the coordinates of the pre-image and image points, they will write rules. A reflection is a mirror image of the shape. Students will reflect figures over the x- and y-axes. 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). In Geometry, a reflection is known as a flip. 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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