how to find coordinates of a point perpendicular to a line?

Question

The point P is at the foot of the perpendicular from the point a(0,3) to the line $y=3x$

1) find the equation of the line AP and find the coordinates of P

I have found the equation of the line which is $3y = x - 9$, but unable to find the coordinates of P. Could anyone guide me? Also, Show that the line $y=3x$ is parallel to the tangent of the graph of $y=x^2 - 7 x +2$ Thanks

Here's a quick guide to writing math on this site. If your questions are more readable people are more likely to respond to them! — najayaz, Mar 21 '15 at 16:27
And there are infinitely many tangents to that graph. Which one are you talking about? — najayaz, Mar 21 '15 at 16:30
@G-man: Probably about the one that is parallel to the line $y=3x$ ;-) — celtschk, Mar 21 '15 at 16:33
@celtschk that's all right but the question still doesn't make sense. — najayaz, Mar 21 '15 at 16:34
@G-man: There's a reason why I ended that comment with a smiley. — celtschk, Mar 21 '15 at 16:35
that's the way the question was given. can anyone help please? — kylie, Mar 21 '15 at 17:00

score 1 · Answer 1 · edited Mar 21 '15 at 17:07

1

Hint:

Your equation of the perpendicular is wrong. The slope parameter of a perpendicular to a straight line $y=mx+q$ is $m'= -\dfrac{1}{m}$.

Correct this mistake and find the intersection point of the two straight lines, that is your $P$.

As noted in the comments your second question is confused. Why?

edited Mar 21 '15 at 17:07

Narasimham

40,495

answered Mar 21 '15 at 16:55

Emilio Novati

62,675

score 1 · Answer 2 · answered Mar 21 '15 at 17:02

1

If AP is the line perpendicular to the line y= 3x, then the slope of AP is $\frac {-1}{3}$.

You are required to check your result again because of the following:-

This means that the equation of AP is 3y + x = some constant, which is found to be 9 by the fact that the line passes through A(0, 3).

To find P, you need to solve the two equations. This will give you P = (0.9, 2.7).

For the second part, there are many points on the given graph. Each point has its own value of slope. Your question did not say which point. This make the comparison with y = 3x impossible. I guess that point is (5, -8).

answered Mar 21 '15 at 17:02

Mick

17,141

Which of the two equations do i need to get P? I have the answers which are 9/10 and 27/10, but i have no idea how to get there.. – kylie Mar 21 '15 at 17:21
One is the equation just found (i.e. 3y + x = 9) and the other is the one that was given (i.e. y = 3x). – Mick Mar 21 '15 at 17:23
sorry to ask again, but i'm confused, what do i need to substitute in order to get the coordinates? – kylie Mar 21 '15 at 17:33
Just put y = 3x in 3y + x = 9 to get 3(3x) + x = 9. – Mick Mar 21 '15 at 17:37

how to find coordinates of a point perpendicular to a line?

2 Answers2