Question

Determine whether the given co-ordinates are the vertices of a triangle

and if yes then state the type of triangle .

(i) A(3, 5), B(4, 7), C(7, 6)​

Answer 1

Answer:

Using the distance formula d=(x2−x1)2+(y2−y1)2, we get

AB2=(2+3)2+(6+4)2=52+102=25+100=125

BC2=(−6,−2)2+(10−6)2=(−8)2+42=64+16=80

CA2=(−6+3)2+(10+4)2=(−3)2+(14)2=9+196=205

i.e., AB2+BC2=125+80=205=CA2

Hence ABC is a right angled triangle since the square of one side is equal to sum of the squares of the other two sides.