Point in a triangle

Geometry Level 4

$\color{#D61F06}{A(-13,14)}$ , $\color{#3D99F6}{B(-3,-5)}$ and $\color{#20A900}{C(7,11)}$ are the vertices of a triangle. The coordinates of the point $P$ inside the triangle $ABC$ such that $\Delta PBC$ is an equilateral triangle is $(p,q)$ .Find $p+q$

The answer is -0.196.

1 solution

Tanishq Varshney
Aug 1, 2015

Slope of line $m_{BC}=\frac{8}{5}$

As $PBC$ is an equilateral triangle

$\text{The perpendicular from P on BC will bisect side BC, let this point be D}$

so $D(2.3)$

$m_{PD}=-\frac{5}{8}$

Length of $BC=\sqrt{356}=2\sqrt{89}$

length of $PD=\frac{\sqrt{3}}{2}BC=\sqrt{89 \times 3}$

Using parametric form we get

$p=2-8\sqrt{3}$ and $q=3+5\sqrt{3}$

Point in a triangle

The answer is -0.196.

1 solution

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