Question 749136: Calculate the area of the triangle with the following vertices:
6. (-3, -3), (0, -3), (1, 1)
7. (8, -2), (-0, -2), (2, -5)
8. .(-9, 0), (-1, 2), (-5, 4)
9. (3, -7), (6, 4), (-2, -3)
10. (-5, -7), (-1, -7), (-3, -4)
Find the area of the parallelogram with the following vertices:
11. (-2, 3), (5, 8), (3, 3), and (0, 8)
12. (-2, 7), (-4, 4), (-11, 4), and (-9, 7)
13. (-6, 6), (-6, 3), (-12, 3), and (-12, 6)
14. (12, -3), (5, -6), (5, -3), and (12, -6)
15. (-2, 2), (-6, 9), (-13, 9), and (-9, 2)
Find the equation of the line that passes through the following points. Put your equation into slope-intercept form:
16. (4, 25), (8, 61)
17. (-8, -1), (0, -1)
18. (3, -41), (1, -9)
19. (-6, -70), (4, 50)
20. (9, -98), (0, 19)
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Calculate the area of the triangle with the following vertices:
6. (-3, -3), (0, -3), (1, 1)
7. (8, -2), (-0, -2), (2, -5)
8. .(-9, 0), (-1, 2), (-5, 4)
9. (3, -7), (6, 4), (-2, -3)
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10. A(-5,-7), B(-1,-7), C(-3,-4)
A...B...C...A
-5 -1 -3 -1
-7 -7 -4 -7
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Get the sum of the diagonal products starting at the upper left.
-5*-7 + -1*-4 + -3*-7 = 35 + 4 + 21 = 60
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Get the sum of the diagonal products starting at the lower left.
-7*-1 + -7*-3 + -4*-1 = 7 + 21 + 4 = 32
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Area = 1/2 the difference = (60 - 32)/2
Area = 14 sq units.
Do the others the same way.
Do the parallelograms below the same way, too. It works for any # of points.
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Find the area of the parallelogram with the following vertices:
11. (-2, 3), (5, 8), (3, 3), and (0, 8)
12. (-2, 7), (-4, 4), (-11, 4), and (-9, 7)
13. (-6, 6), (-6, 3), (-12, 3), and (-12, 6)
14. (12, -3), (5, -6), (5, -3), and (12, -6)
15. (-2, 2), (-6, 9), (-13, 9), and (-9, 2)
Find the equation of the line that passes through the following points. Put your equation into slope-intercept form:
16. (4, 25), (8, 61)
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Using determinants:
|x +y 1|
|4 25 1| = 0
|8 61 1|
Note: + is for alignment
x*(25-61) - y*(4-8) + 1*(244-200) = 0
-36x + 4y + 44 = 0
y = 9x - 11
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Do the others the same way.
17. (-8, -1), (0, -1)
18. (3, -41), (1, -9)
19. (-6, -70), (4, 50)
20. (9, -98), (0, 19)
I'll be glad to check your work if you email via the Thank You note.
PS Don't put a space after the comma in the points.
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