Question

Show that the points P (1,1) Q(-1,-1) R(√-3, √3) are a part of a equilateral triangle. show steps

Answer 1

Distance formula

d=√(x2-x1)²+(y2-y1)²

Step-by-step explanation:

Given

P(1,1) Q(-1,-1) R(√-3, √3) are a part of a equilateral ∆

Distance formula

d=√(x2-x1)²+(y2-y1)²

PQ = √{ ( -1 - 1 )² +( -1 - 1 )² }

= √{ ( -2 )² + ( -2 )²}

= √{ 4 + 4 } = √8

PQ = 2√2

similarly for QR & RP

QR = √{ ( [-√3] - [-1] )² + ( √3 - [-1] )² }

= √{ (-√3 +1 )² + ( √3 +1 )² }

= √{ 3 + 1 - 2√3 + 3 + 1 + 2√3

=√8

QR = 2√2

RP= √{ ( 1 - [-√3] )² +( 1 - √3 )² }

= √{ (1 + √3 )² +( 1 - √3 )² }

= √{ 1+ 3 + 2√3 + 1+ 3 - 2√3 }

=√8

RP = 2√2

PQ = QR = RP

Hence

P (1,1) Q(-1,-1) R(√-3, √3) are a part of a equilateral triangle.