The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is

(A) (0, 1)   (B) (0, –1)   (C) (–1, 0)   (D) (1, 0)

 

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Question 14 The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is (A) (0, 1) (B) (0, –1) (C) (–1, 0) (D) (1, 0) Since ABCD is a parallelogram It’s Diagonals bisect each other Therefore, Mid point of AC = Mid point of BD ((−2 + 8)/2,(3 + 3)/2)=((6 + 𝑥)/2,(7 + 𝑦)/2) (6/2,6/2)=((6 + 𝑥)/2,(7 + 𝑦)/2) Comparing x-coordinate 6/2=(6 + 𝑥)/2 6 = 6 + x x = 0 Comparing y-coordinate 6/2=(7 + 𝑦)/2 6 = 7 + y y = −1 ∴ Coordinates of point D is (0, −1) So, the correct answer is (B)

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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.