Year 11 Maths - Methods Coordinate geometry and linear relations

Parallel And Perpendicular Lines

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Questions

Question 1

17652

The equation of the line that passes through the point \((1, - 1)\) and is perpendicular to the line \(y = 5x + 2\) is?

Answer

\(x + 5y + 4 = 0\)

Worked Solution

\begin{align}
&m_{1}=5,\; m_{2}=-\frac{1}{5}\\
&\begin{aligned}
y-y_{1} &=m\left(x-x_{1}\right) \\
y-(-1) &=-\frac{1}{5}(x-1) \\
5(y+1) &=-(x-1) \\
5 y+5 &=-x+1
\end{aligned}\\
&\rightarrow x+5 y+4=0
\end{align}

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