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 Question from Kgaugelo: a triangle has the vertices A(-4;-3),B(x;y)and C(2;1). Determine the coordinates of B if the equation of the line BC is y=5x-9

I don't like the way this problem is worded because the letters $x$ and $y$ are used in two different ways. When the problem states that $B(x;y)$ is one of the vertices of a triangle then $x$ and $y$ represent two fixed but unknown numbers. When the equation of the line is written $y = 5x - 9$ the letters $x$ and $y$ represent variables that are the first and second coordinates of any point on the line. I want to reword the problem to say

a triangle has the vertices A(-4;-3),B(d;e)and C(2;1). Determine the coordinates of B if the equation of the line BC is y=5x-9

Since $B(d;e)$ is a point on the line $BC$ its coordinated satisfy the equation of the line and hence

$e = 5d - 9.$

If you knew something else about the triangle you may be able to write a second equation involving $d$ and $e$ and then solve the two equations for $d$ and $e.$ Do you know anything else about the triangle?

Harley

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