If the vertices of a parallelogram PQRS taken in order are P(3,4),

Q(-2,3) and R(-3,-2), then the coordinates of its fourth vertex S are

(a) (-2,-1)   (b) (-2,-3)   (c) (2,-1)   (d) (1,2)

 

This question is similar to Question 14 - NCERT Exemplar - MCQ

 

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Transcript

Question 5 If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), then the coordinates of its fourth vertex S are (a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2) Since PQRS is a parallelogram It’s Diagonals bisect each other Therefore, Mid point of PR = Mid point of QS ((3 + (−3) )/2,(4 + (−2) )/2)=((−2 + 𝑥)/2,(3 + 𝑦)/2) (0, 2/2)=((−2 + 𝑥)/2,(3 + 𝑦)/2) (0, 2/2)=((−2 + 𝑥)/2,(3 + 𝑦)/2) Comparing x-coordinate 0=(−2 + 𝑥)/2 0 = −2 + x x = 2 Comparing y-coordinate 2/2=(3 + 𝑦)/2 2 = 3 + y y = −1 ∴ Coordinates of point S is (2, −1) So, the correct answer is (c)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.