Question

Let PQR be an equilateral triangle in which coordinate of Q and R are (5, 0) and (-5, 0) respectively. Find the coordinates of the point P. Find area of ∆.​

Answer 1

Step-by-step explanation:

Given PQR is an equilateral triangle in which Q(0,2) and R(0,−2).

Let (x,0) be the coordinates of P. [∵P lies on x axis. So y-coordinate is zero.]

PQ=PR=QR=2+2=4

OQ=2 [from figure]

In POQ,

PQ

2

=OP

2

+OQ

2

[Pythagoras theorem]

4

2

=OP

2

+2

2

OP

2

=4

2

−2

2

OP

2

=16−4

OP

2

=12

OP=√(4×3)=2√3

Hence the coordinates of P are (2√3,0).