Draw the triangle with vertices A = (2, 2), B = (-1, 3), and C = (0, 0). By regarding it as half of a parallelogram, explain why its area equals area (ABC) = 1 ¦det [_ 2 2 -1 3 Move the third vertex to C = (1, -4) and justify the formula 1 x1 У1 1 2 2 1 1 area (ABC) = det x2 y2 1 = det -1 3 2 2 X3 Уз 1 1 -4 1 }] Hint: Subtracting the last row from each of the others leaves 2 2 1 1 60 16 det -1 3 1 = det -2 7 0 = det -2 7 1 -4 1 1 -41 Sketch A' = (1, 6), B' = (-2, 7), C' = (0, 0) and their relation to A, B, C.
Draw the triangle with vertices A = (2, 2), B = (-1, 3), and C = (0, 0). By regarding it as half of a parallelogram, explain why its area equals area (ABC) = 1 ¦det [_ 2 2 -1 3 Move the third vertex to C = (1, -4) and justify the formula 1 x1 У1 1 2 2 1 1 area (ABC) = det x2 y2 1 = det -1 3 2 2 X3 Уз 1 1 -4 1 }] Hint: Subtracting the last row from each of the others leaves 2 2 1 1 60 16 det -1 3 1 = det -2 7 0 = det -2 7 1 -4 1 1 -41 Sketch A' = (1, 6), B' = (-2, 7), C' = (0, 0) and their relation to A, B, C.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![Draw the triangle with vertices A = (2, 2), B = (-1, 3), and C = (0, 0). By
regarding it as half of a parallelogram, explain why its area equals
area (ABC) =
1
¦det [_
2 2
-1 3
Move the third vertex to C = (1, -4) and justify the formula
1
x1 У1 1
2
2
1
1
area (ABC) =
det x2
y2 1 = det
-1
3
2
2
X3
Уз 1
1
-4
1
}]
Hint: Subtracting the last row from each of the others leaves
2
2
1
1
60
16
det
-1
3
1
= det
-2
7 0
= det
-2 7
1 -4 1
1
-41
Sketch A' = (1, 6), B' = (-2, 7), C' = (0, 0) and their relation to A, B, C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad0d55fe-d83b-4711-86a1-cee8ecea510f%2Fdf5948ee-5f9a-446f-8d27-030db033d044%2Foi7eync_processed.png&w=3840&q=75)
Transcribed Image Text:Draw the triangle with vertices A = (2, 2), B = (-1, 3), and C = (0, 0). By
regarding it as half of a parallelogram, explain why its area equals
area (ABC) =
1
¦det [_
2 2
-1 3
Move the third vertex to C = (1, -4) and justify the formula
1
x1 У1 1
2
2
1
1
area (ABC) =
det x2
y2 1 = det
-1
3
2
2
X3
Уз 1
1
-4
1
}]
Hint: Subtracting the last row from each of the others leaves
2
2
1
1
60
16
det
-1
3
1
= det
-2
7 0
= det
-2 7
1 -4 1
1
-41
Sketch A' = (1, 6), B' = (-2, 7), C' = (0, 0) and their relation to A, B, C.
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