Additional Mathematics – Straight-line graphs | e-Consult

Step 1 – Midpoint of CD:

• \(\bigl(\frac{-4+2}{2},\frac{1+9}{2}\bigr)=(-1,5)\).

Step 2 – Slope of CD:

• \(m_{CD}= \frac{9-1}{2-(-4)}=\frac{8}{6}= \frac{4}{3}\).

Step 3 – Slope of perpendicular bisector:

• Negative reciprocal: \(m_{\perp}= -\frac{3}{4}\).

Step 4 – Equation using point‑slope form through \((-1,5)\):

• \(y-5 = -\frac{3}{4}(x+1)\).
• Multiply by 4: \(4(y-5)= -3(x+1)\).
• Expand: \(4y-20 = -3x-3\).
• Re‑arrange to standard form: \(3x+4y-17=0\).