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

Find the two points that divide the line joining A(-4, 5) and B(8, -1) into three equal parts.

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

Find the two points that divide the line joining $A(-4, 5)$ and $B(8, -1)$ into three equal parts.

Need a reminder? The key ideaShow

The point dividing the line from $(x_1, y_1)$ to $(x_2, y_2)$ in the ratio $m : n$ is $\left(\dfrac{m x_2 + n x_1}{m + n}, \dfrac{m y_2 + n y_1}{m + n}\right)$ . The midpoint is the average of the two 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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← Find the point P that divides the line from A(-2, 3) to B(8, -2) in the ratio 3 : 2.Say what kind of triangle has the corners A(2, 1), B(6, 4) and C(-1, 5). →

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