Question

9. ( 20 points.) In the Cartesian plane model of Euclidean geometry, which of the triples of points (a)-(d) below, if any, are the vertices of a right triangle? (a) (2, 1), (7,0),(5, 7). (b) (102,51), (101, 48), (105,57). (e) (2,1),(4,0),(4,7). (d) (102. - 49), (104,-50). (105,-43). (c) None

Answer 1

Answer » A triangle is said to be . e a right brangle By Pythagoneen theorem Vuu (hyfotimuse ) ? - Horfendisuda'+ 1 Bases in option (a) vester = P = (2,1) QF 7,0. P=(2, 1) QF 7,0) R=(5,7) PIQUE 147-270+10+)2 = 36 QiRi= 117-53467-032 = 153 Rip, = √ (6-2)²+(1-13² rus so it is not satisfied hythagorean theorem so it is not a right triangle. ofition (b) vester = P2 = (10251) Qu=404,48) RF (10557) P2Q2 = 1104-102376148)2 = 113 Q₂ R2 = 105-104 34157-48)2 = 482 RzP2= 105-10234157-512=145 so it is also not satisfied fythagorean theoren so it is also not a sight triangle. Oltion (c) vestere = P3= (2,1) Q3 = (40) =(47) B3Q3= 14-284 (1-032 = 15 Off R3 = 114-42762-032=/49 R3P3 = √ (4-2)} (1-12 = 140 il is also not satisfied hythagorean theore see it is also not a right triangle m

option and - (to -45) Se (let -56) R4 (105-43) PyQlu = 1104-10 294(50-49) ? - 15 QuPy = J los-14460-43)2 = 150 Puly = (05-1034(43-49= 45 So by Ptt Pythagorum theoren Ou Ry)? (Pu Qu)?+ (RuPyJ2 (150) = 15.3+ jas)? so it satisfied Pythagorean theorem so they are the verter of right triangle Oftion 'ď is correct Answers