Simple coordinate geomety problem

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In summary, the conversation discusses a coordinate geometry problem where the equation of lines passing through a given point and having a specific distance from another point needs to be found. The conversation also touches upon the solution method and the possibility of missing a solution.
  • #1
silent_hunter
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I'm not sure where to post this. So I'm posting in the General Math section.This is a simple coordinate geometry problem: We have to find the equation of line(s) passing through the point (7,17) and having a distance of 6 units from the point(1,9).

Now I'm posting my approach:
the equation of line passing through(7,17) and having slope m is
y-17=m(x-7)
or, mx-y-7m-17=0
now the line have a distance of 6 units from point(1,9).
so [itex]\frac{m-9-7m+17}{\sqrt{m^2 +1}}[/itex]=[itex]\pm[/itex]6
or,(6m-8)2 =36(m2 +1)
or, m=7/24
so the equation of line becomes 7x-24y+359 =0
This way we get only line.But if you draw it in a graph paper,you'll see that there should be another line which is x-7=0 which is parallel to the y-axis.(draw a circle of radius 6 from (1,9) and then draw tangent from (7,17) to the circle).
I think we can't get the second one because it has undefined slope.
My question is how can I get the second line without plotting in graph?
 
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  • #2
hi silent_hunter! :smile:

(try using the X2 button just above the Reply box :wink:)

you lost half the solutions when you took the square-root of this line …
silent_hunter said:
or,(6m-8)^2 =36(m^2 +1)
or, m=7/24

you should have put the intermediate step (6m-8) = ±36(m2 +1) :wink:
 
  • #3
tiny-tim said:
you should have put the intermediate step (6m-8) = ±36(m2 +1) :wink:

thanks for your reply :smile:
(6m-8)2 =36(m2 +1)
in that step I squared both sides of the equation ,so the ± sign should go away.
 
  • #4
sorry, i got that wrong :redface:

this is where you missed a solution …
silent_hunter said:
the equation of line passing through(7,17) and having slope m is
y-17=m(x-7)
or, mx-y-7m=17=0

… you missed out m = ∞ ! :smile:​
 
  • #5
tiny-tim said:
sorry, i got that wrong :redface:

this is where you missed a solution …
… you missed out m = ∞ ! :smile:​

sorry I made a typing mistake. :blushing:
Its mx-y-7m-17=0 but I didn't get what you said. Would you please elaborate?Thanks.
 
  • #6
one of the two lines is x = 7, isn't it?

(with slope ∞)

that doesn't come up for any m in mx-y-7m-17=0 :wink:
 
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  • #7
if you think, (y-9)^2+(x-1)^2=36 then

if you think of it as (y-9)^2 + (x-1)^2 = 36

then:

y=cos(3(x-1))+15.91 or so should hit twice.

I'll bet some kind of absolute value function would hit three times.
 

FAQ: Simple coordinate geomety problem

1. What is coordinate geometry?

Coordinate geometry is a branch of mathematics that deals with the study of geometric figures using numerical coordinates. It involves representing points, lines, curves, and shapes on a graph using a set of numbers.

2. How do I plot points on a coordinate plane?

To plot points on a coordinate plane, you need to have two numbers - the x-coordinate and the y-coordinate. The x-coordinate represents the horizontal distance from the origin (0,0) and the y-coordinate represents the vertical distance. Plot the point by starting at the origin and moving horizontally and vertically according to the given coordinates.

3. How do I find the distance between two points on a coordinate plane?

To find the distance between two points on a coordinate plane, you can use the distance formula: d = √((x2-x1)^2 + (y2-y1)^2). Simply plug in the coordinates of the two points into the formula to calculate the distance.

4. What is the slope of a line in coordinate geometry?

The slope of a line in coordinate geometry is a measure of its steepness. It is represented by the letter m and is calculated by dividing the change in y-coordinates by the change in x-coordinates between any two points on the line. The slope can be positive, negative, zero, or undefined depending on the direction and steepness of the line.

5. How can I determine if two lines are parallel or perpendicular?

To determine if two lines are parallel, you can compare their slopes. If the slopes are equal, then the lines are parallel. To determine if two lines are perpendicular, you can calculate the slope of each line using the slope formula. If the product of the slopes is -1, then the lines are perpendicular.

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