The area of a triangle can be calculated using the determinant of the matrix. From the image below: P2(x2, y2) P,(x1, Yı) P3(X3, Y3) A(x1, 0) B(x2, 0) C(x3, 0) The coordinates of the image points above are arranged into a matrix A as follows: [x1_ yı A = |x2 Y2 Lx3 Уз and let the last column contain the number 1. The formula for finding the area of a triangle is: 1 area of triangle = 5 det (A) If the coordinates of the point P1 = (-1.4), P2 = (3, 1), and P3 = (2,6): A. Plug the coordinates of these points into matrix A. B. Using the first-row expansion method, find the minor and calculate the cofactor for each element of the first row. C. Compute the determinant of matrix A.
The area of a triangle can be calculated using the determinant of the matrix. From the image below: P2(x2, y2) P,(x1, Yı) P3(X3, Y3) A(x1, 0) B(x2, 0) C(x3, 0) The coordinates of the image points above are arranged into a matrix A as follows: [x1_ yı A = |x2 Y2 Lx3 Уз and let the last column contain the number 1. The formula for finding the area of a triangle is: 1 area of triangle = 5 det (A) If the coordinates of the point P1 = (-1.4), P2 = (3, 1), and P3 = (2,6): A. Plug the coordinates of these points into matrix A. B. Using the first-row expansion method, find the minor and calculate the cofactor for each element of the first row. C. Compute the determinant of matrix A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The area of a triangle can be calculated using the determinant of the matrix. From the image below:
P2(x2, y2)
P(x1, yı)
P3(x3, y3)
A(x1, 0)
B(x2, 0) C(x3, 0)
The coordinates of the image points above are arranged into a matrix A as follows:
[X1 y1
1-
A = |X2 y2
1
Lx3 Уз
1
and let the last column contain the number 1.
The formula for finding the area of a triangle is:
area of triangle
det (A)
2
If the coordinates of the point P = (-1.4), P2 = (3, 1), and P3 = (2,6):
A. Plug the coordinates of these points into matrix A.
B. Using the first-row expansion method, find the minor and calculate the cofactor for each element
of the first row.
C. Compute the determinant of matrix A.
D. Calculate the area of the triangle.
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