Year 11 locus question (1 Viewer)

kpad5991 · Aug 18, 2017

Hey, can someone explain how to use the distance formula to find the locus of a point that moves so that it is equidistant from the lines y = x +3 and y = x + 5. I can show it using a diagram but how do you find the equation using the distance formula??? Thanks in advance.

1729 · Aug 18, 2017

kpad5991 said:
Hey, can someone explain how to use the distance formula to find the locus of a point that moves so that it is equidistant from the lines y = x +3 and y = x + 5. I can show it using a diagram but how do you find the equation using the distance formula??? Thanks in advance.

$$\noindent By inspection it is $y = x + 4$ but we can also use the perpendicular distance formula using $P(x,y)$, $x - y + 5 = 0$ and $x - y + 3 = 0$. \\ \begin{align*}\quad \frac{|x-y+3|}{\sqrt{2}} &= \frac{|x-y+5|}{\sqrt{2}} \\ |x-y+3| &= |x-y+5| \\ x - y + 3 &= -(x-y+5) \\ y &= x+4 \end{align*}$

Year 11 locus question (1 Viewer)

kpad5991

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