General Procedure
for finding Orthocenter
1. Start with triangle with coordinates A, B, and C.
2. Draw triangle carefully
3. Find slopes of lines AB, AC, and BC
4. Use negative reciprocal of slope of AB and Point C in point slope formula to find equation of altitude #1.
5. Use negative reciprocal of slope of AC and Point B in point slope formula to find equation of altitude #2.
6. Use negative reciprocal of slope of BC and Point A in point slope formula to find equation of altitude #3.
7. Use substitution method to find the x and y coordinates at point where Altitudes #1, #2, and #3 all meet
General Procedure
for finding Circumcenter
1. Start with triangle with coordinates A, B, and C.
2. Draw triangle carefully
3. Find slopes of lines AB, AC, and BC
4. Find midpoints of segment AB (call it D), segment AC (call it E), and segment BC (call it F)
5. Use Point D and negative reciprocal of slope of AB to find equation of perp. Bisector #1
6. Use Point E and negative reciprocal of slope of AC to find equation of perp. Bisector #2
7. Use Point F and negative reciprocal of slope of BC to find equation of perp. Bisector #3
8. Use substitution method to find the x and y coordinates at point where Perpendicular Bisectors #1, #2, and #3 all meet
General Procedure
for finding Centroid
1. Start with triangle with coordinates A, B, and C.
2. Draw triangle carefully and correctly
3. Find midpoints of segment AB (call it D), segment AC (call it E), and segment BC (call it F)
4. Use Point D and Point C to find the slope of Median CD
5. Use Point E and Point B to find the slope of Median BE
6. Use Point F and Point A to find the slope of Median AF
7. Use the slope of median CD and either Point C or Point D to find the equation of Median CD
8. Use the slope of median BE and either Point B or Point E to find the equation of Median BE
9. Use the slope of median AF and either Point A or Point F to find the equation of Median AF
10. Use substitution method to find the x and y coordinates at point where Perpendicular Bisectors #1, #2, and #3 all meet
Consider the
following coordinate triangles:
1. A (0,0) B (4,4) C (7,1)
2. A (0,0) B (10, 25) C (20, -5)
3. A (0,0) B (5, 0) C
(-4, 7)
4. A (0,0) B (-10, 2) C. (-3, 15)
5. A (0,0) B (5, -5) C.
(7, 7)
For Triangle
6, use the following clues to determine a unique triangle. Please mark the
numbers that you are using in the last column.
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X-coordinate of Point A |
The negative of the number of letters in your first name |
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Y-coordinate of Point A |
The number of letters in your mom’s first name |
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X-coordinate of Point B |
Your age divided by 5 |
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Y-coordinate of Point B |
Your height in inches divided by 10 |
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X-coordinate of Point C |
The last digit of your cell number |
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Y-coordinate of Point C |
The negative of the first digit of your cell number |
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For each triangle complete the following table
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Triangle |
Acute, Obtuse, or Right |
Equilateral, Scalene, or Isosceles |
Orthocenter |
Circumcenter |
Centroid |
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#1 |
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#2 |
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#3 |
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#4 |
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#5 |
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#6 |
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