Question

pqr is an equilateral triangle in the co-ordinate q and r as (0,4) and (0,-4). find the co-ordinate of the vertex p

Answer 1

As Q & R lie on y axis
P lies on x axis say with coordinates (x,0)
QR=8 units
x=+_4 (sq rt 3)
so P (4sq rt 3,0) or (-4sq rt 3,0)

Answer 2

Answer:

coordinate of the vertex p is (6.93,0)

Step-by-step explanation:

From the attached figure, the distance between Q and R is 4 + 4 =8

Hence, QR = 8

Since, it is an equilateral triangle. Hence, all the sides are equal.

Therefore, PQ = PR = QR = 8

Now, vertex p is on the x axis. Hence, the y coordinate is 0.

Let the vertex p is (x,0)

Thus, we have

PQ = 8

$\sqrt{0-4)^2+(x-0)^2}=8\\\\16+x^2=8^2\\x^2=64-16\\x^2=48\\x=\sqrt{48}\\x=6.93$

Thus, coordinate of the vertex p is (6.93,0)