University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2023
Views:

82

Pages:

2
Author:

Clint W.

Pradice Мedions ond Altitudes А 1n дАВС, Х is the centroid. 1.UC�\f=IS,findCXandXW: 2. U ВХ= 8, find BYandXY. ВУ CX=10;XW=S = 12;ХУ = 4 3. U XZ= 3, findA.XandAZ. АХ= 6; AZ = 9 ls АВ а medi.a11, an altitude, or neilher?Explain. 4. Median; АВ Ьisects the opposite side. S. А 6. Altitude; АВ is perpendicular to the opposite side. 7. А Neither; АВ is not rpendicular to nor does i t blsect the opposite side. � � 2 В А Altitude; АВ is perpendicular to the opposite side. 3 Coordinate Geometry Find the onhocenter of дАВС. 8. А(2, О), В(2, 4), С(б, О) (2, О) 10. Name the centroid. и Q 9. A(I, 1), В(З, 4), С(6, 1) (3, 3) 11. Name the orthocenter. Х А Dra,v а triangle that fits the given description. Then construct the centroid and the orthoceoter. 12. equilateral дСDЕ Sample: See art. с Е 13. acute isosceles дХУZ Sample: See art. х Or'lhoc�nt�r z;-<,:;��.:>t-;y Practice 1conIinuedJ Мedians and Altitudes In Exercises 14--18, name each segment. 14. а median in дАВС ёJ 1 S. an alritude for дАВС АН С Н G В 16. а median in дАНС /Н 17. an alritude for дАНВ АН or ВН 18. an alritude for дАНG АН or GH 19. А(О, О), В(О, -2), С(-3, О). Find the orthocenter of дАВС. (О, О) 20. Cut а large isosceles triangle out of papeL Paper-fold to construct the medians and the alritudes. Ho,v are the alritude to the base and the median to the Ьаsе related? Тhеу are the same. 21. ln ,vblch kind of triangle is the centroid at the same point as the orthocenter? equilateral = 22. Р is the ceotroid of дМNО. МР 14х + Ву. Write expressions to representPRandAfR. PR = lx + 4у; MR = 21х + 12у = 23. F is the oentroid of ЛАСЕ. AD 15х2 + Зу. \\frite expressions to representAFandFD. AF= 1ох2 + 2y;FD = sx2 + у 24. Use coordinate geometry to prove the follmving statement. Given: дАВС; А(с, tf), В(с, е), CfJ, е) Pro"·e: The circumcenter of дАВС is а point on the triangle. Sample: The drcumcenter is the intersectlon of the perpendicular blsectors of а triangle. The midpoints of АВ and ВС are (с, d and (' е). So, the equations of their perpendicular blsectors are х = с; f and у= d; I!. Тheir intersection is (с; ', d; I!}, which is the midpoint of АС !� ! '•