Year 11 Maths - Methods Linear Relations

Coordinate Geometry of the Straight Line

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Questions

Question 1

17651

Given that \(A( - 3, - 12),\) \(\,B(0,3)\,\) and \(C(4,b)\) are collinear then the value of \(b\) is?

Answer

\(b = 23\)

Worked Solution

\begin{align}
&m_{AB}=\frac{3-(-12)}{0-(-3)}=\frac{15}{3}=5\\
&m_{BC}=\frac{b-3}{4-0}=\frac{b-3}{4}\\
&\text{Collinear when } m_{AB}=m_{BC}\\
&\begin{aligned}
\rightarrow \;\frac{b-3}{4}&=5 \\
b&=23
\end{aligned}
\end{align}

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