Intersection between the line AB and and the perpendicular line which contains the point C.

perpendicular_intersection.ts

interface Point {
    readonly x: number;
    readonly y: number;
}

/**
 * This function returns the intersection between the line AB
 * and the perpendicular line that contains the point C.
 */
function intersection(a: Point, b: Point, c: Point): Point {
    let d0 = b.x - a.x;
    let d1 = b.y - a.y;
    let d2 = c.x - a.x;
    let d3 = c.y - a.y;
    let divisor = d0 * d0 + d1 * d1;
    let x = divisor > 0 ? (d0 * d2 + d1 * d3) / divisor : 0;

    return {x: a.x + d0 * x, y: a.y + d1 * x};
}

let d = intersection({ x: 0, y: 0 }, { x: 10, y: 10 }, { x: 5, y: 0 });
alert(`(${d.x}, ${d.y})`);