Question

The point P= (x,-1/7) lies on the unit circle shown below. What is the value of x in simplest form? ​

Answer 1

Answer:

$x^2 + \frac{1}{49} =1$

And solving for x we got:

$x^2 = 1- \frac{1}{49}$

$x^2 = \frac{48}{49}$

And taking square root we got:

$x = \sqrt{\frac{48}{49}}= \frac{\sqrt{48}}{7} = \frac{4\sqrt{3}}{7}$

Step-by-step explanation:

For this case we have the following point given $P(x , -1/7)$

And we want to find the value of x, since P lies on the unitray circle if we find the distance from P to the center of the unitary circle (0,0) we need to get 1. Using the definition of Euclidean distance that means:

$d = \sqrt{(x -0)^2 +(-1/7 -0)^2}=1$

And if we square both sides of the last equation we got:

$x^2 + \frac{1}{49} =1$

And solving for x we got:

$x^2 = 1- \frac{1}{49}$

$x^2 = \frac{48}{49}$

And taking square root we got:

$x = \sqrt{\frac{48}{49}}= \frac{\sqrt{48}}{7} = \frac{4\sqrt{3}}{7}$