Question

in the given figure, pqr is an equilateral triangle with coordinates q and R has (-2,0) and(2,0) resp. find the coordinates of a vertex p​

Answer 1

Answer:

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).

Answer 2

Answer:

APQR is an equilateral triangle

⇒ PQ = PR = QR

⇒ PQ = QR

→ PQ = 4

OQ = 2

In right triangle POQ, OP² + 0Q² = PQ2 |By Pythagoras Theorem OP² + (2)² = (4)2

⇒ OP = 2√2

⇒ P = (0,2√3)

Step-by-step explanation:

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