Find equation of line through origin which is perpendicular

[tehmatriks]

Homework Statement

Find the slope of the line through x(2, -3) and y(1, 2).
What is the slope of any line perpendicular to xy?
Hence, find the equation of the line through the origin and which is perpendicular to xy.

Homework Equations

slope formula:
m = y₂ - y₁/ x₂ - x₁


equaltion of the line:
y - y₁ = m(x - x₁)

The Attempt at a Solution

m = y₂ - y₁/ x₂ - x₁
m = 2 + 3/ 1 - 2
m = 5/-1
m = -5
slope of any line perpendicular = 1/5

Eq. of line:
y - y₁ = m(x - x₁)
y + 3 = 1/5(x - 2)
5y + 15 = x - 2
x - 5y - 2 - 15 = 0
x - 5y - 17 = 0


i know that's wrong, just need a push in the right direction

 

[LCKurtz]

Homework Statement

Find the slope of the line through x(2, -3) and y(1, 2).
What is the slope of any line perpendicular to xy?
Hence, find the equation of the line through the origin and which is perpendicular to xy.

Homework Equations

slope formula:
m = y₂ - y₁/ x₂ - x₁


equaltion of the line:
y - y₁ = m(x - x₁)

The Attempt at a Solution

m = y₂ - y₁/ x₂ - x₁
m = 2 + 3/ 1 - 2
m = 5/-1
m = -5
slope of any line perpendicular = 1/5

Eq. of line:
y - y₁ = m(x - x₁)
y + 3 = 1/5(x - 2)
5y + 15 = x - 2
x - 5y - 2 - 15 = 0
x - 5y - 17 = 0


i know that's wrong, just need a push in the right direction

You want the line through the origin, not through your original point.

 

[symbolipoint]

What do you mean?

1. Homework Statement
Find the slope of the line through x(2, -3) and y(1, 2).
What is the slope of any line perpendicular to xy?
Hence, find the equation of the line through the origin and which is perpendicular to xy.

Which points are that you refer? The point (2, -3) and the point (1, 2), or the point (2, 1) and the point (-3, 2)?

 

[thearn]

Homework Statement

Find the slope of the line through x(2, -3) and y(1, 2).
What is the slope of any line perpendicular to xy?
Hence, find the equation of the line through the origin and which is perpendicular to xy.

Homework Equations

slope formula:
m = y₂ - y₁/ x₂ - x₁equaltion of the line:
y - y₁ = m(x - x₁)

The Attempt at a Solution

m = y₂ - y₁/ x₂ - x₁
m = 2 + 3/ 1 - 2
m = 5/-1
m = -5
slope of any line perpendicular = 1/5

Eq. of line:
y - y₁ = m(x - x₁)
y + 3 = 1/5(x - 2)
5y + 15 = x - 2
x - 5y - 2 - 15 = 0
x - 5y - 17 = 0i know that's wrong, just need a push in the right direction

I believe that your problem is occurring at the point where you plug in 1/5 as the slope in the equation of the line. This is inaccurate because 1/5 is not the slope of the equation of the line. As you had shown above that, -5 was the slope that you found from using the slope formula. You use the slope of -5 in the equation of the line. Which should look like this. y+3=-5(x-2). This leads to y=-5x+7 . I advise graphing it be hand so it is easier to understand. Once you are at this point, the problem says find a line that is perpendicular about the origin (x and y=0). From here since you know that the problem wants you to find the perpendicular line that intersects the line with the equation x-, drop the line to the origin of x and y=0 so the perpendicular line that bisects y=-5x+7 is y= 1/5x. 1/5 is put in at this point in the equation because know that 1/5 is the slope that will give us the perpendicular line that we are looking for. Hopefully this helped.

 

[LCKurtz]

I believe that your problem is occurring at the point where you plug in 1/5 as the slope in the equation of the line. This is inaccurate because 1/5 is not the slope of the equation of the line. As you had shown above that, -5 was the slope that you found from using the slope formula. You use the slope of -5 in the equation of the line. Which should look like this. y+3=-5(x-2). This leads to y=-5x+7 . I advise graphing it be hand so it is easier to understand. Once you are at this point, the problem says find a line that is perpendicular about the origin (x and y=0). From here since you know that the problem wants you to find the perpendicular line that intersects the line with the equation x-, drop the line to the origin of x and y=0 so the perpendicular line that bisects y=-5x+7 is y= 1/5x. 1/5 is put in at this point in the equation because know that 1/5 is the slope that will give us the perpendicular line that we are looking for. Hopefully this helped.

Oh good grief! He has the correct slope of 1/5 for the perpendicular. All he needs is the equation of a line through the origin with that slope.

 

[tehmatriks]

You want the line through the origin, not through your original point.

well this is embarrassing, it took me having to draw a graph to realize where the origin was, and then it all came back to me...thanks