3. One of the geometrical properties receiving incomplete treatment in the Elements is the plane separation property. This exercise is meant to verify a special case. Suppose we are given two points in the coordinate plane (a, b) and (c, d) with the first one below the x-axis (so b < 0) and the second above it (so d > 0). Show that the line joining these two points meets the x-axis in some point (u, 0) such that one of the following holds: a < u < ¢ a > u > C [Hint: Draw a picture, hold the first point fixed, and plot several possibilities for the second point.]
3. One of the geometrical properties receiving incomplete treatment in the Elements is the plane separation property. This exercise is meant to verify a special case. Suppose we are given two points in the coordinate plane (a, b) and (c, d) with the first one below the x-axis (so b < 0) and the second above it (so d > 0). Show that the line joining these two points meets the x-axis in some point (u, 0) such that one of the following holds: a < u < ¢ a > u > C [Hint: Draw a picture, hold the first point fixed, and plot several possibilities for the second point.]
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 13AEXP
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Question
![3.
One of the geometrical properties receiving incomplete treatment
in the Elements is the plane separation property. This exercise is meant to verify a
special case.
Suppose we are given two points in the coordinate plane (a, b) and (c, d) with the first
one below the x-axis (so b < 0) and the second above it (so d > 0). Show that the line
joining these two points meets the x-axis in some point (u, 0) such that one of the following
holds:
a < u < ¢
a > u > C
[Hint: Draw a picture, hold the first point fixed, and plot several possibilities for the
second point.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b0185de-0645-4c2a-aea4-e046d61ab5cb%2F5610a7e0-c02f-465d-a77e-74abd60de70f%2Fyu12ldf.jpeg&w=3840&q=75)
Transcribed Image Text:3.
One of the geometrical properties receiving incomplete treatment
in the Elements is the plane separation property. This exercise is meant to verify a
special case.
Suppose we are given two points in the coordinate plane (a, b) and (c, d) with the first
one below the x-axis (so b < 0) and the second above it (so d > 0). Show that the line
joining these two points meets the x-axis in some point (u, 0) such that one of the following
holds:
a < u < ¢
a > u > C
[Hint: Draw a picture, hold the first point fixed, and plot several possibilities for the
second point.]
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