![]() 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. Step 2: Extend the line segment in the same direction and by the same measure. Since the reflection line is perfectly horizontal, a line perpendicular to it would be perfectly vertical. So the equation of this line is y = (-1/7)x + 65/7. Step 1: Extend a perpendicular line segment from A to the reflection line and measure it. 11) x y Q N R E Q N R E rotation 90° clockwise about the origin 12) x y S U X T S U X T rotation 180° about the origin 13) x y V Z T V Z T rotation 180° about the origin 14) x y H Y T H Y T rotation 180° about the origin-2-Create your own worksheets like this one with Infinite Pre-Algebra. So the desired line has an equation of the form y = (-1/7)x + b. Write a rule to describe each transformation. 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). And since a rotation matrix commutes with its transpose, it is a normal matrix, so can be diagonalized. ![]() We are guaranteed that the characteristic polynomial will have degree n and thus n eigenvalues. So we first find the equation of the line through (2,9) that is perpendicular to the line y = 7x + 2. In Euclidean geometry, a rotation is an example of an isometry. In other words, switch x and y and make y negative. 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. The most common rotations are 180 or 90 turns, and occasionally, 270 turns, about the origin, and affect each point of a figure as follows: Rotations About The Origin 90 Degree Rotation When rotating a point 90 degrees counterclockwise about the origin our point A (x,y) becomes A' (-y,x). A positive degree rotation runs counter clockwise and a negative degree rotation runs clockwise. Then we can algebraically find point C, which is the intersection of these two lines. What are Rotations Rotations are a type of transformation in geometry where we take a point, line, or shape and rotate it clockwise or counterclockwise, usually by 90,180, 270, -90, -180, or -270. 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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