The vertices of a parallelogram in order are A (1, 2), B (4, y), C (x, 6) and D (3, 5). Then (x, y) is

(a) (6, 3)   (b) (3, 6)   (c) (5, 6)   (d) (1, 4)

 

This question is inspired from Ex 7.2, 6 (NCERT) - Chapter 7 Class 10 - Coordinate Geometry

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  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

Transcript

Question 29 The vertices of a parallelogram in order are A (1, 2), B (4, y), C (x, 6) and D (3, 5). Then (x, y) is (a) (6, 3) (b) (3, 6) (c) (5, 6) (d) (1, 4) Given A(1, 2), B(4, y), C(x, 6), D(3, 5) We know that Diagonals of parallelogram bisect each other So, O is the mid−point of AC & BD Finding mid−point of AC Coordinates of O = ((1 + 𝑥)/2,(2 + 6)/2) = ((1 + 𝑥)/2,8/2) = ((𝟏 + 𝒙)/𝟐,𝟒) Finding mid−point of BD Coordinates of O = ((3 + 4)/2,(5 + 𝑦)/2) = (𝟕/𝟐,(5 + 𝑦)/2) Now, ((𝟏 + 𝒙)/𝟐,𝟒) = (𝟕/𝟐,(5 + 𝑦)/2) Comparing x-coordinate (1 + 𝑥)/2 = 7/2 (1 + x) = 7 x = 7 – 1 x = 6 Comparing x-coordinate 4 = (𝑦 + 5)/2 4 × 2 = y + 5 8 – 5 = y y = 3 ∴ (x, y) = (6, 3) So, the correct answer is (a)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.