Purchase Solution

Lines and Intersections

Not what you're looking for?

Ask Custom Question

Incidence Geometry: Give proofs for the following:

i.For every line there is at least one point not lying on it.

ii.For every point, there is at least one line not passing through it

iii.For every point P, there exist at least two distinct lines through P.

Purchase this Solution
Solution Summary

Step-by-step proofs are provided to all the lines and intersections statements.

Solution Preview

Incidence Geometry
Give proofs for the following:

i. For every line there is at least one point not lying on it.
Proof:
We know that there exist three non-collinear points. Let us call these P,Q, and R. Let p be any line. Then at least one out of P, Q, R is does not lie l, since P,Q, and R all coincident with p contradicts the fact that they are non-collinear.

ii. For every ...

Solution provided by:
Sandhya Sharma, MSc
Education
  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
Recent Feedback
  • "Perfect, thank you so much!!! I will definitely request you in the future! You are amazing!"
  • "Thank you. "
  • "Thank you so much I have two more that I need your help with if your available."
  • "Thank you, I was wondering why you rejected me the first time."
  • "Thanks again."
Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Real and Non-Real Affine Intersection Points and Their Multiplicities

    a2 be the number of distinct affine real intersections with multiplicity two, let b be the numberof distint complex non-real affine intersections and let c be the number of intersection points at infinity counting multiplicities.

  • Geometry problems

    This is a series of geometry questions involving unions and intersections of lines, line segments, and angles; complementary and supplementary angles; parallel lines and transversals; perimeter, area, circumference, and volume.

  • Inequalities, domain and Intersections of Lines

    Inequalities, domains, and intersections of lines are examined.

  • Line Intersections

    Intersecting lines are investigated. The solution is detailed and well presented.

  • Systems of linear equations

    What are the co-ordinates of the point of intersection of lines m and n? c. Write the co-ordinates of the intersections of lines m and n with the x-axis. d. Write the co-ordinates of the intersection of lines m and n with the y-axis.

  • Graphing Linear Functions and Finding the Point of Intersection

    Write the co-ordinates of the intersections of lines m and n with the x-axis. f. Write the co-ordinates of the intersection of lines m and n with the y-axis. Please see the attached file for the complete solution. Thanks for using BrainMass.

  • Equations and Vertical Lines.

    What are the co-ordinates of the point of intersection of lines M and N? c. Write the co-ordinates of the intersections of lines M and N with the x-axis. d. Write the co-ordinates of the intersection of lines M and N with the y-axis.

  • Analytical geometry problem regarding lines intersections.

    we get two equations for the two possible lines: Analytical geometry of problems regarding lines and intersections are determined.

  • Equations of lines

    What are the co-ordinates of the point of intersection of lines M and N? c. Write the co-ordinates of the intersections of lines M and N with the x-axis. d. Write the co-ordinates of the intersection of lines M and N with the y-axis.

View More Related Solutions