Originally Posted by

**earboth** I've done this question in a completely different way:

1. Draw a sketch of the lines $\displaystyle a:y = \frac32 x -5$ and $\displaystyle b:y=-x+12$ and the point A.

2. Determine the point of intersection of a and b: $\displaystyle a\cap b = \{S\}$

3. Determine the equation of a line parallel to a through A $\displaystyle p:y=\frac32 x +\frac12$

4. Determine the point of intersection of p and b: $\displaystyle p\cap b = \{R\}$

5. You reach S if you go from R 2.2 units right and 2.2 units down. Now go from S 4.4 units right and 4.4 units down and you are at Q:$\displaystyle Q\left(\frac{56}5\ ,\ \frac45 \right)$.

6. Determine the equation of the line AQ = l: $\displaystyle y = -\frac2{17} x + \frac{36}{17}$. Determine the point of intersection of $\displaystyle l \cap a=\{P\}$

7. I've got $\displaystyle P\left(\frac{22}5\ ,\ \frac85 \right)$