Finding the value of a point on a straight line

Question

Hi i'm really bad in math , i need your help for that, i'm looking for a way to find the star point value lining on a straight line as on the picture posted .

Answer 1

The black line segment appears to be the part of the line $$ y = 0.52 + \frac{-0.52}{0.29}x $$ in the first quadrant. The gray line intersecting it at the star appears to be part of the line $y = x$.

If appearances are not deceiving, then the two coordinates of the star are the same and we can get one of them by substituting the one linear equation into the other: $$ x = 0.52 + \frac{-0.52}{0.29}x $$ and solving for the surviving variable \begin{align*} x &= 0.52 + \frac{-0.52}{0.29}x \\ x - \frac{-0.52}{0.29}x &= 0.52 \\ x\left(1 - \frac{-0.52}{0.29}\right) &= 0.52 \\ x &= \frac{0.52}{1 - \frac{-0.52}{0.29}} \cdot \frac{0.29}{0.29} \\ x &= \frac{0.52 \cdot 0.29}{0.29 + 0.52} \\ x &= 0.186{\dots} \text{.} \end{align*}

So the coordinates of the star appear to be $(0.186{\dots}, 0.186{\dots})$.