How to normalize the vertices array in OpenGL? - opengl

Question

I am trying to draw a triangle on my OpenGL window.
What I want is that I specify three points and OpenGL draws the triangle based on that, the problem is, for that I have to convert the OpenGL coordinates to normalized screen coordinates.
It would look something like this, after normalized:--
Here the three ( X, Y )s (points of triangle) will be specified by the user using three vectors.
But the problem is that the vertices(red points shown in the example figure) are in perspective or default OpenGL coordinates, but I want to make a 2D triangle, so I would not require 3D coordinates for drawing it.
Can you show me a way to convert the vertices into normalized coordinates (from 0.0 to 1.0 or -1.0, in both axis to 0.0 to "width or height of the screen respective to the axis", in both axis)
The code of the shaders(for the triangle):-
::Vertex Shader::
#version 330 core
layout (location = 0) in vec3 position;
void main()
{
gl_Position = vec4(position.x, position.y, position.z, 1.0);
}
::Fragment Shader::
#version 330 core
out vec4 color;
void main()
{
color = vec4(1.0f, 0.5f, 0.2f, 1.0f);
}
What the vertices array looks like(Sample Code):-
GLfloat x = 0; // First X Point
GLfloat y = 0; // First Y Point
GLfloat x1 = 10; // Second X Point
GLfloat y1 = 10; // Second Y Point
GLfloat x2 = 0; // Third X Point
GLfloat y2 = 10; // Third Y Point
GLfloat vertices[] =
{
2 * x / WIDTH - 1, 2 * y / HEIGHT - 1, 0.0f, // Left
2 * x1 / WIDTH - 1, 2 * y1 / HEIGHT - 1, 0.0f, // Right
2 * x2 / WIDTH - 1, 2 * y2 / HEIGHT - 1, 0.0f // Top
};