Coordinate Geometry

Find the area of a triangle whose vertices are $(1, -1), (-4, 6)$ and $(-3, -5)$.

Determine the ratio in which the line segment joining the points $(-3, 10)$ and $(6, -8)$ is divided by $(-1, 6)$.

Find the relation between $x$ and $y$ such that the point $(x, y)$ is equidistant from the points $(3, 6)$ and $(-3, 4)$.

Find the area of a triangle whose vertices are $(1, -1), (-4, 6)$ and $(-3, -5)$. Also, derive and explain the formula used to calculate the area of a triangle in coordinate geometry.