Additional Mathematics – Straight-line graphs | e-Consult

Midpoint of AB:

• \(\bigl(\frac{1+7}{2},\frac{2+8}{2}\bigr)= (4,5)\).

Slope of AB:

• \(m_{AB}= \frac{8-2}{7-1}= \frac{6}{6}=1\).

Perpendicular slope:

• \(m_{\perp}= -1\) (negative reciprocal of 1).

Equation of perpendicular bisector through (4,5):

• Point‑slope: \(y-5 = -1(x-4)\).
• Simplify: \(y = -x +9\).

Substitute the x‑coordinate of P (x = 3):

• \(k = y = -3 + 9 = 6\).

Thus, \(k = 6\).