Is it in the polygon?
Charcoal, 52 50 bytes
≔⪪Ａ²θＦ⟦Ｅ³§θ⊖ιθ✂θ¹⟧⊞υ↔ΣＥι⁻×§κ⁰§§ι⊕λ¹×§κ¹§§ι⊕λ⁰⁼⊟υΣυ

Try it online! Link is to verbose version of code. Explanation:
≔⪪Ａ²θ

Split the input into pairs of coordinates.
Ｆ⟦Ｅ³§θ⊖ιθ✂θ¹⟧

Calculate the area of three polygons: the one formed by taking the last, first and second points; the one formed from all of the points (including the test point); the one formed from all of the points except the test point.
⊞υ↔ΣＥι⁻×§κ⁰§§ι⊕λ¹×§κ¹§§ι⊕λ⁰

Use the shoelace formula to calculate the area of that polygon.
⁼⊟υΣυ

Check whether the last area equals the sum of the first two. If this is the case, then the point lies within the polygon.