Answer:
A. Inside the circle
Step-by-step explanation:
K(0, 0), U (6, - 4), V ([tex] \sqrt 2,\: 7)[/tex]
In order to determine whether point V lie inside, outside or on the circle, first we will find the distances between points K & U and then K & V.
KU would be radius of the circle.
- If KV is smaller than KU, then V will lie inside.
- If KV is larger than KU, then V will lie outside
- And If KV = KU, then V will lie ion the circle.
[tex]d(KU) = \sqrt{ {(6 - 0)}^{2} + {( - 4 - 0)}^{2} } \\ = \sqrt{ {6}^{2} + {( - 4)}^{2} } \\ = \sqrt{36 + 16} \\ \red{ \bold{ d(KU)= \sqrt{52} }} \\ \\ d(KV) = \sqrt{ {( \sqrt{2} - 0)}^{2} + {( 7 - 0)}^{2} } \\ = \sqrt{ {( \sqrt{2)} }^{2} + {(7)}^{2} } \\ = \sqrt{2 + 49} \\ \purple{ \bold{ d(KV)= \sqrt{51} }} \\ \\ \because \: d(KU) > d(KV) \\ [/tex]
Hence point V lie inside of the circle.
