Ex 7.1, 4
Check whether (5, –2), (6, 4) and (7, –2) are the vertices of an isosceles triangle.
In an isosceles triangle, any 2 of the 3 sides are equal.
Let the three points be P(5, −2), Q(6, 4) & R(7, −2)
In order to be isosceles,
Either PQ = PR
or
PQ = QR
or
PR = QR
We calculate the value of PQ, QR & PR by distance formula
Calculating PQ
PQ = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √(( 6 −5)2+(4 −(−2))2)
= √(12+(6)2)
= √(1+36)
= √37
Calculating QR
QR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √(( 7 −6)2+(−2 −4)2)
= √(12+(−6)2)
= √(1+36)
= √37
Calculating PR
PR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √(( 7 −5)2+(−2 −(−2))2)
= √(22+(−2+2)2)
Calculating QR
QR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √(( 7 −6)2+(−2 −4)2)
= √(12+(−6)2)
= √(1+36)
= √37
Calculating PR
PR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √(( 7 −5)2+(−2 −(−2))2)
= √(22+(−2+2)2)
Calculating QR
QR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √(( 7 −6)2+(−2 −4)2)
= √(12+(−6)2)
= √(1+36)
= √37
Calculating PR
PR = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2)
= √(( 7 −5)2+(−2 −(−2))2)
= √(22+(−2+2)2)
= √(2^2+0^2 )
= √(2^2 )
= 2
Hence, PQ = √37, QR = √37, PR = 2
Since PQ = QR
It satisfies the condition of isosceles triangle
Hence, PQR is an isosceles triangle

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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