HardMathematicsHigh School (9–10)GeneralCoordinate Geometry › Distance, Midpoint and Section FormulaeNumerical

For what value of k do A(-1, 4), B(1, 1) and C(5, k) lie on one straight line?

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

For what value of $k$ do $A(-1, 4)$ , $B(1, 1)$ and $C(5, k)$ lie on one straight line?

Need a reminder? The key ideaShow

Compare the squares of the sides to name a triangle: equal sides make it isosceles, and $a^2 + b^2 = c^2$ gives a right angle. Area $= \tfrac{1}{2}\left|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)\right|$ , which is $0$ for collinear points.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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