Check if a point is inside a quadrilateral

To know if a Point is inside a square, the following must be checked:

that xPoint is greater than xsquare and that xPoint is less than xSquare+base

yPoint is greater than ySquare and yPoint is less than ySquare+height

In the following example I check with 2 points for the two cases (point inside the square and the opposite case).

var canvas = document.getElementById('canvas');
var ctx = canvas.getContext('2d');
var point = {
  'x': 2,
  'y': 20
};
var point2 = {
  'x': 20,
  'y': 20
};

var cuadrado = {
  'x': 10,
  'y': 10,
  'base': 50,
  'altura': 100
};


function putPixel(ctx, x, y, color) {
  ctx.fillStyle = color;
  ctx.fillRect(x, y, 2, 2);
}

function draw(x, y, base, altura) {
  ctx.strokeRect(x, y, base, altura);
}

draw(cuadrado.x, cuadrado.y, cuadrado.base, cuadrado.altura);
putPixel(ctx, point.x, point.y, 'blue');
putPixel(ctx, point2.x, point2.y, 'red');
console.log(comprobar(point, cuadrado));
console.log(comprobar(point2, cuadrado));

function comprobar(punto, cuadrado) {
  if (punto.x > cuadrado.x && punto.x < cuadrado.x + cuadrado.base && punto.y > cuadrado.y && punto.y < cuadrado.y + cuadrado.altura) {
    return true;
  }
  return false;
}

<canvas id="canvas">
</canvas>

Do you consider that if it is touching the border, is it inside or outside? This is important at the moment of knowing if it is < or <= what you want to catch as inside or outside.

To begin with, in a square it holds:

base == altura

So I'm assuming you're talking about any quadrilateral, a rectangle.

AX you add the base and you get X+b. AY you add the height and you get Y+a.

You have to explain well and know 1. Your coordinate system, where does the value of X and Y increase? to the right and up? right and down? Because the sign of the operations has to do with this.

Generally, the point (x1, y1) will be inside the square if: (considering that the point on the border is included in the square)

(x1 <= X+b) AND (x1 >= X) AND (y1 <= Y+a) AND (y1 >= Y)

And considering that the point on the border is NOT included in the square:

(x1 < X+b) AND (x1 > X) AND (y1 < Y+a) AND (y1 > Y)

But you have to take into account your coordinate system.

All the best