Distance between two points on a line given by parametric equation

Question

Can anyone please help me about this.

The parametric equations of the line are $x = x_1 + t \cos \dfrac{\pi}{3}$ and $y = y_1 + t \sin \dfrac{\pi}{3}$. Two points on the line are $A(x_1,y_1)$ and $B(x_2,y_2)$. I should find the distance $AB$ in terms of $t$.

Answer 1

Hint :

$$A\equiv(x_1,y_1)$$ $$B\equiv(x_2,y_2)\equiv(x_1+\frac{t}{2},y_1+\frac{\sqrt{3}t}{2})$$

$$AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$