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)
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.
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