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 March 31st, 2018, 06:29 AM #1 Senior Member   Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry [ASK] Reflection of a Line by Another Line The reflection of the line 5x - 7y - 13 = 0 by the line y = -x is .... A. 7x + 5y - 13 = 0 B. 7x + 5y + 13 = 0 C. 7x - 5y - 13 = 0 D. 7x - 5y + 13 = 0 E. 7y + 5x + 13 = 0 This one I totally have no idea. Like, at all. March 31st, 2018, 11:36 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 No idea? Do you know what a line is? Do you know what symmetric means? That's quite a lot to be getting on with! A line reflects into a line. And two points determine a line. Let $\displaystyle (0, y_0)$ be any point on the y-axis. Then "reflection in the line y- x" maps it to the point $\displaystyle (-y_0, 0)$. And any point $\displaystyle (x_0, 0)$ on the x-axis is mapped to the point $\displaystyle (0, -x_0)$. Let x= 0 in 5x- 7y- 13= 0. then -7y- 13= 0 so y= -13/7. The point (0, -13/7) is on the given line and reflection in the line y= -x maps it to (13/7, 0). Let y= 0 in 5x- 7y- 13= 0. Then 5x- 13= 0 so x= 13/5. The point (13/5, 0) is o the given line and reflection in the line y= -x maps it to (0, -13/5). So the question is just to find the equation of the line through (13/7, 0) and (0, -13/5). Any non-vertical line can be written in the form y= mx+ b. Taking x= 13/7, y= 0, we have 13m/7+ b= 0. Taking x= 0, y= -13/5, m(0)+b= b= -13/5. Then 13m/7- 13/5= 0 so 13m/7= 13/5. m/7= 1/5 so m= 7/5. The equation of the line is y= (7/5)x- 13/5. 5y= 7x- 13 so 7x- 5y= 13. March 31st, 2018, 05:08 PM   #3
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 Originally Posted by Country Boy No idea? Do you know what a line is? Do you know what symmetric means? That's quite a lot to be getting on with!
I know, in fact I can solve that graphically by manually find the reflection's equation, but I didn't know how to do it algebraically. Anyway, thanks for your help. Tags line, reflection Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post cfern87 Calculus 0 October 27th, 2017 08:10 PM nomad609 Calculus 0 October 23rd, 2016 11:39 AM randomgamernerd Geometry 2 November 18th, 2015 10:02 AM xaosman Applied Math 0 July 2nd, 2013 10:24 AM math12345 Algebra 3 April 3rd, 2011 10:54 AM

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