The line $\ell$ has a gradient of $3$.

The distinct points $A(a,6)$ and $B(2,b)$ lie on $\ell$.

1. Given that $A$ and $B$ are equidistant from the point $C(3,7)$, find an equation for the line $\ell$.

2. Prove that $\mathrm{△}ABC$ is a right-angled triangle.

3. Find the area of triangle $\mathrm{△}ABC$.

Because $A$ and $B$ lie on $\ell$, the gradient $m_{AB}$ must equal the gradient of $\ell$.

The length of $AC$ is equal to the length of $BC$. You will need the distance formula.

A diagram will help: