Triangle $ABC$ has vertices $A(1,1)$, $B(5,3)$ and $C(4,5)$. Show that the triangle is right

Question

Triangle $ABC$ has vertices $A(1,1)$, $B(5,3)$ and $C(4,5)$. Show that the triangle is right-angled at $B$.[2] Find the exact lengths of $AB$ and $BC$.[2] Hence, calculate the area of triangle $ABC$.[1]

Accepted Answer

(a) Gradient product $-1$ (b) $2\sqrt5$, $\sqrt5$ units (c) $5$ square units

A right angle from coordinates

A right angle from coordinates

Solution:

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