Solved

Coordinate Geometry-Finding ratio of a point splitting a line

Posted on 2016-10-23
4
61 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

Is Your Active Directory as Secure as You Think?

More than 75% of all records are compromised because of the loss or theft of a privileged credential. Experts have been exploring Active Directory infrastructure to identify key threats and establish best practices for keeping data safe. Attend this month’s webinar to learn more.

Question has a verified solution.

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

Suggested Solutions

Title # Comments Views Activity
Sampling 3 44
Linear algebra 3 62
Math question 3 76
Triangles - Calculating angles 7 63
Lithium-ion batteries area cornerstone of today's portable electronic devices, and even though they are relied upon heavily, their chemistry and origin are not of common knowledge. This article is about a device on which every smartphone, laptop, an…
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
Learn how to create flexible layouts using relative units in CSS.  New relative units added in CSS3 include vw(viewports width), vh(viewports height), vmin(minimum of viewports height and width), and vmax (maximum of viewports height and width).
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.

863 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

Need Help in Real-Time?

Connect with top rated Experts

19 Experts available now in Live!

Get 1:1 Help Now