Answer:
k = 7
Step-by-step explanation:
Find the coordinates of P using the midpoint formula
P = [[tex]\frac{1}{2}[/tex](2 + 5), [tex]\frac{1}{2}[/tex](- 1 - 6) ]
= ( [tex]\frac{7}{2}[/tex], - [tex]\frac{7}{2}[/tex])
Since the line passes through P the the coordinates of P make the equation true.
Substitute the coordinates of P into the equation
2 × [tex]\frac{7}{2}[/tex] + 4 × - [tex]\frac{7}{2}[/tex] + k = 0, that is
7 - 14 + k = 0
- 7 + k = 0 ( add 7 to both sides )
k = 7
