Solved

Coordinate Geometry-Finding ratio of a point splitting a line

Posted on 2016-10-23
4
68 Views
Last Modified: 2016-10-26
Coordinate Geometry

Question: In what ratio is the line joining the points (4,2) and (3,-5) divided by the x-axis? Also, find the coordinates of the point of intersection.

Solution: Let the required ratio be(K:1) and the point on the x-axis be (x,0).
Taking (4,2)=(x1:y1) and (3,-5)=(x2:y2)
Since, y=(ky1+y1)/(k+1)
The ratio of m:n is 2:5 and the value of x is 26/7
(I am sorry that i am unable to use subscript in this web page)


My question is y is the solution using K:1 as the ratio. Secondly why is the solution starting with solving the value of Y (ordinate) and not X.

Kindly help.
0
Comment
Question by:Excellearner
  • 2
4 Comments
 
LVL 27

Expert Comment

by:d-glitch
ID: 41856046
You need to make a drawing to visualize the problem.
And you need to remember that the equation for the x-axis is y=0.
So there are two units of the line above the x-axis and five below.

Complete the big right triangle [with sidebar x=4 and y=-5] to calculate the ratios.
0
 
LVL 27

Assisted Solution

by:aburr
aburr earned 250 total points
ID: 41856352
d-glitch's suggestion to draw a diagram is VERY good. Once you do so, almost no calculation is needed.
note the y ratio is 2/5. that means that the x ratio is 2/5.
so the x intercept is 3 + the ratio of the one x unit to get to 4. Your diagram will tell you how to do it.
( 3 + 5/7 = the 26/7 value of x which you got.
A good look at your diagram will let you fill in the steps to get your answer. If it is not self-evident, ask.
-
as far as your question "Secondly why is the solution starting with solving the value of Y (ordinate) and not X."
I have not the faintest idea.
Diagrams often make things easy.
0
 

Author Comment

by:Excellearner
ID: 41856668
d-glitch and aburr, thank you both for your comments.

The attached includes the diagram and the workings.

For now i will not argue with why Y has been chosen instead of X. But can you help me understand why K:1 (that is one in alpha and the other in numeric) has been used instead of m:n ratio.

Thank you

*I did not understand this statement: so the x intercept is 3 + the ratio of the one x unit to get to 4. Your diagram will tell you how to do it.
( 3 + 5/7 = the 26/7 value of x which you got
IMG_4007-coordinate-g.JPG
0
 
LVL 27

Accepted Solution

by:
d-glitch earned 250 total points
ID: 41857013
You diagram is okay, but not quite to scale.  The rise is 7, the run is 1, so it should be closer to vertical.

They do not mention K:1 in the problem, and they did not really use it in the solution.  I think it is intended as a hint to use ratios.  Or maybe because the run of the line segment is 1.

Back to the x-axis.
  • Q1.   What is the equation of the x-axis?  
           A2.    y = 0     (Nothing about x)

  • Q2.   What does the x-axis do?
           A2.   It divides the real plane into three regions:
                   y = 0  on the axis
                   y > 0  above the axis
                   y < 0  below the axis     (Once again, nothing about x)

The term x-axis refers to a particular line.  Make a good drawing and don't worry about the terminology.
0

Featured Post

Master Your Team's Linux and Cloud Stack

Come see why top tech companies like Mailchimp and Media Temple use Linux Academy to build their employee training programs.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
Odd Behavior 5 61
Binomial distribution 2 55
Convert a 1D array of timestamps into a 2D array (time-group-mid-point, frequency) 10 79
calendar source - options.. 10 50
Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…

773 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question