Question

the point P = (x, -5/7) lies on the unit curcle shown below. What is the value of x in the simplest form?

Answer 1

`x =\± (2√(6))/(7)`

Explanation:

The question has missing details as the unit circle is not shown, However, I'll solve on a general terms.

Given

`P = (x,-(5)/(7))`

Required

Determine the possible value of x

Since point p lies on the unit circle, we'll solve this question using the following unit circle formula:

`x^2 + y^2 = 1`

Substitute -5/7 for y

`x^2 + (-(5)/(7))^2 = 1`

`x^2 + (25)/(49) = 1`

Collect Like Terms

`x^2 =1- (25)/(49)`

Take LCM

`x^2 =(49 -25)/(49)`

`x^2 =(24)/(49)`

Take the square root of both sides

`x =\± \sqrt{(24)/(49)}`

`x = \±(√(24))/(7)`

`x = \±(√(4*6))/(7)`

Split

`x = \±(√(4)*√(6))/(7)`

`x =\± (2*√(6))/(7)`

`x =\± (2√(6))/(7)`