CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]

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Question 29 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by

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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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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