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Example 1 Do the points (3, 2), (–2, –3) and (2, 3) form a triangle? If so, name the type of triangle formed. Let the three points be P(3, 2), Q(−2, −3) & R(2, 3) We find the distances PQ, QR, and PR Calculating PQ x1 = 3 , y1 = 2 x2 = −2 , y2 = −3 PQ = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( −2 −3)2+(−3 −2)2) = √((−5)2+(−5)2) = √((5)2+(5)2) = √(2(5)2) = √2 × 5 = 5√𝟐 = 5 × 1.414 = 7.07 Calculating QR x1 = −2 , y1 = −3 x2 = 2 , y2 = 3 QR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 2 −(−2))2+(3 −(−3))2) = √(( 2+2)2+(3+3)2) = √(( 4)2+(6)2) = √(16+36) = √52 = √(4 × 13) = 𝟐√𝟏𝟑 = 7.21 Calculating PR x1 = 3 , y1 = 2 x2 = 2 , y2 = 3 PR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 3 −2)2+(2 −3)2) = √((1)2+(−1)2) = √(( 1)2+(1)2) = √(1+1) = √𝟐 = 1.141 Hence, PQ = 7.07 , QR = 7. 21, PR = 1.41 Since the sum of any two of these distances is greater than the third distance Therefore, P, Q, R form a triangle Finding which type of Triangle Since, PQ = √50 , QR = √52, PR = √2 So, PQ2 + PR2 = (√50)2 + (√2)2 = 50 + 2 = 52 = (QR)2 Therefore, PQ2 + PR2 = QR2 So, PQR is a right angled triangle

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.