February 25th, 2017, 03:43 PM  #1 
Newbie Joined: Feb 2017 From: Moscow, Russia Posts: 2 Thanks: 0  Functions
Can anybody please explain to me how to solve this. Find the perpendicular distance from (0, 0) to the line x+y+k=0.

February 25th, 2017, 04:08 PM  #2  
Senior Member Joined: May 2016 From: USA Posts: 883 Thanks: 353  Quote:
What is the slope of any perpendicular to that line? What is the equation of the perpendicular line that includes the origin? At what point do the lines intersect? How would you calculate the distance from that point to the origin?  
February 26th, 2017, 01:33 PM  #3 
Newbie Joined: Feb 2017 From: Moscow, Russia Posts: 2 Thanks: 0 
1) I don't know. The graph will be a straight line. 2) 90 degree angle. 3) Again I don't know. 4) k? 5) I can't plot the graph and k point. If you could walk me through it, I would appreciate a lot. 
February 26th, 2017, 01:49 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 1,696 Thanks: 861  Quote:
$y = (1)x  k$ can you tell what the slope is now? 2) I think Jeff1 is asking you for the actual slope of a line that is perpendicular to this line. You need to figure out the slope of the original line in order to do that. You should know the formula for the slope of a perpendicular to a line with slope $m$. Look it up. 3) given the slope you figured out in (2), and the fact that $(0,0)$ is on this line, use the pointslope formula to come up with the formula for this perpendicular line. 4) just set the two lines equal to one another and solve for $(x,y)$ 5) the distance between 2 points is $d=\sqrt{(x_2x_1)^2+(y_2y_1)^2}$ now suppose that $(x_1,y_1)=(0,0)$, simplify above  
February 26th, 2017, 02:11 PM  #5  
Senior Member Joined: May 2016 From: USA Posts: 883 Thanks: 353  Quote:
(2) Actually, a slope of 1 or  1 means that the line forms an angle of 45 degrees where it intersects the axes. Useful to know, but not critical. (3) As romsek explained, put the given equation into slope intercept form. Then reread my point 1. That will tell you the slope of the given line. There is an easy formula (that you need to learn) to go from the slope of a given line to the slope of any line perpendicular to the given line. So the slope alone will not tell you what the equation of the perpendicular is. (4) There are many perpendiculars to a given line. You are interested in the one that includes the origin. So you know the yintercept (which is what?) of the perpendicular that you want, and, once you have answered question 3, you know the slope too. That gives you the complete equation of the perpendicular. (5) The next to the last step is to find the point of intersection of two lines, one of which has equation y = m + bx and the other of which has equation y = nx + c. You solve those two simultaneous equations and find the coordinates of the point of intersection. (6) Now you are all set to use the distance formula. Please try to go through these steps and show us what you did. Then we can confirm whether your answer is correct, and, if not, we can point out your errors.  

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