It is not.
In order for the point to be on the unit circle, the sum of squares of the coordinates must be 1. You have (1² +3²)/17 = 10/17, not 1.
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The point (1/√17, 4/√17) would be on the unit circle.
Answer:
The given point does not lie on the unit circle.
Step-by-step explanation:
We are given the following information in the question:
A unit circle is a circle with radius of 1 unit and has its center on the origin that is with coordinates (0,0).
Thus, the equation of unit circle is of the form:
[tex]\text{Equation of circle}\\(x-h)^2 = (y-k)^2 + r^2\\\text{where (h,k) is the cenyer of the circle, r is the radius of the circle}\\\Rightarrow \text{Equation of unit cirle}\\(x-0)^2 + (y-0)^2 = (1)^2\\x^2 + y^2 = 1[/tex]
Now, we are given the point
[tex]\bigg(\displaystyle\frac{-1}{\sqrt{17}},\frac{3}{\sqrt{17}}}\bigg)[/tex]
Putting this values in the equation of unit circle, we have:
[tex]\bigg(\displaystyle\frac{-1}{\sqrt{17}},\frac{3}{\sqrt{17}}}\bigg)\\\\x^2 + y^2 = 1\\\bigg(\displaystyle\frac{-1}{\sqrt{17}}\bigg)^2 + \bigg(\frac{3}{\sqrt{17}}\bigg)^2 = \frac{1}{17} + \frac{9}{17} = \frac{10}{17} \neq 1[/tex]
Thus, the given point does not lie on the unit circle.
