Dividing triangle into two triangles

Geometry Level 3

Concider the triangle $ABC$ as shown in figure. Find the coordinates $(x,y)$ of point $D$ that divides triangle $ABC$ into two triangles $ABD$ and $ACD$ such that the area of $ACD$ is double the area of triangle $ABD$ . Report your answer as $(x-y)$ .

The answer is 3.

1 solution

Michael Mendrin
Dec 4, 2017

Both triangles ABD and ACD have a common altitude, so lengths CD=2DB. Hence, the coordinates x, y are

$x=\dfrac{2}{3}(10-5)+5=\dfrac{25}{3}$
$y=\dfrac{2}{3}(4-8)+4=\dfrac{16}{3}$

so that $x-y=3$

Dividing triangle into two triangles

The answer is 3.

1 solution

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