For three points on the plane (x1, y1), (x2, y2) and (x3, y3) show that thedeterminant of| x1 y1 1 | | x2 y2 1 | | x3 y3 1 | is proportional to the area of the triangle whose corners are the three points. If these points lie on a straight line, what is the value of the determinant? Does this give a useful test to tell whether three points lie on a line? Why do you think so? For three points on the plane (x1, y1), (x2, y2) and (x3, y3) show that thedeterminant ofX1 yi1X2 y2 1Хз уз 1is proportional to the area of the triangle whose corners are the three points. If thesepoints lie on a straight line, what is the value of the determinant? Does this give a usefultest to tell whether three points lie on a line? Why do you think so?

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Answered: For three points on the plane (x1, y1),…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 7AEXP

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For three points on the plane (x1, y1), (x2, y2) and (x3, y3) show that the
determinant of
| x1 y1 1 |
| x2 y2 1 |
| x3 y3 1 |

is proportional to the area of the triangle whose corners are the three points. If these points lie on a straight line, what is the value of the determinant? Does this give a useful test to tell whether three points lie on a line? Why do you think so?

For three points on the plane (x1, y1), (x2, y2) and (x3, y3) show that the
determinant of
X1 yi
1
X2 y2 1
Хз уз 1
is proportional to the area of the triangle whose corners are the three points. If these
points lie on a straight line, what is the value of the determinant? Does this give a useful
test to tell whether three points lie on a line? Why do you think so?

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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