Ex 7.1, 6
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Let the points be
A (4, 5), B (7, 6)
C (4, 3), D (1, 2)
We find the distances AB, BC, CD & AD
By using distance formula
Finding AB
AB = √((𝑥2 −𝑥1)2+(𝑦2 −1)2)
= √(( 7 −4)2+(6 −5)2)
= √((3)2+(1)2)
= √(9+1)
= √10
Finding BC
BC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √(( 4 −7)2+(3 −6)2)
= √((−3)2+(−3)2)
= √((−3)2+(−3)2)
= √((3)2+(3)2)
= √(9+9)
= √18
Finding CD
CD = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √(( 1 −4)2+(2 −3)2)
= √((−3)2+(−1)2)
= √((3)2+(1)2)
= √(9+1)
= √10
Finding AD
AD = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √(( 1 −4)2+(2 −5)2)
= √((−3)2+(−3)2)
= √((3)2+(3)2)
= √(9+9)
= √18
Since, AB = CD = √10
& AD = BC = √18
Since both pairs of opposite sides of quadrilateral are equal,
it would be a parallelogram

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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