Check if the Full-back J(5,-3) and centre-back I(-4,6) are equidistant from forward C(0,1) and if C is the mid-point of IJ.

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We need to check if C is equidistant from J and I And C is mid-point of IJ Doing this one by one Check if C (0, 1) is equidistant from I (−4, 6) and J (5, −3) To prove if point C is equidistant from I & J We need to prove CI = CJ Since CI = CJ ∴ C is equidistant from I and J Finding CI CI = √(( −𝟒 −𝟎)𝟐+(𝟔−𝟏)𝟐) = √((−4)2+(5)2) = √(16+25 ) = √𝟒𝟏 Finding CJ CJ = √(( 𝟓 −𝟎)𝟐+(−𝟑−𝟏)𝟐) = √((5)2+(−4)2) = √(25+16 ) = √𝟒𝟏 Check if C (0, 1) is midpoint of I (−4, 6) and J (5, −3) If C is mid-point of IJ Coordinates of C = ((𝑥1 + 𝑥2)/2,(𝑦1 +𝑦2)/2) (0, 1) = ((−𝟒 + 𝟓)/𝟐,(𝟔 + (−𝟑))/𝟐) (0, 1) = (1/2,3/2) Since LHS ≠ RHS ∴ C is NOT the mid-point of IJ Now, AC = BC √(𝒂𝟐−𝟒𝒂+𝟖) = √(𝒂𝟐−𝟏𝟒𝒂+𝟔𝟓) Squaring both sides (√(𝑎2−4𝑎+8) " )2 = (" √(𝑎2−14𝑎+65))^2 𝒂𝟐−𝟒𝒂+𝟖 = 𝒂𝟐−𝟏𝟒𝒂+𝟔𝟓 −4a + 8 = −14a + 65 −4a + 14a = 65 − 8 10a = 57 a = 57/10 a = 5.7

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.