Help with improving my rect-rect collision detection

Processing Coding Questions
1 
int ellipseRadius = 40;

int r = 0;
int b = 0;
int g = 0;

int rectPowerShowSize = 1;

float xVel = 1;
float yVel = 1;


//images
pImage img;

void setup() {
	size(800, 400);
	background(0);
	frameRate(60);
	img = loadImage('Golf_grass');
}

void draw() {
	int rectRightEdge = ellipseXPos + ellipseRadius/2;
	int rectLeftEdge = ellipseXPos - ellipseRadius/2;
	
	if (gameStage == 0) {
	rectMode(CENTER);
		fill(200, 200);
		rect(width/2, 160, 120, 55);
textSize(30);
		textAlign(CENTER);
		fill(255, 255, 0);
text("START", width/2, 175); 
		
		if (mousePressed) {
			gameStage = 1;
			
		}
		
		
		
		
	}
	
	
	
	
	if (gameStage == 1) {     // the game
imageMode(CENTER);
	image(img, width/2, height/2);
		img.resize(800, 400);
	//background(0)
	fill(255);
	ellipseXPos = ellipseXPos + xVel;		
  ellipseYPos = ellipseYPos + yVel;	
	
	rect(ellipseXPos, ellipseYPos, ellipseRadius, ellipseRadius);
	rect(width/2, height/2, 50, 800);
	xVel = xVel*0.94;
	yVel = yVel*0.94;
	
	if (dist(ellipseXPos, ellipseYPos, width/2, height/2) < ellipseRadius/2 +50/2) {
	//	background(255);
	}

	//when touch left and right edge, changes speed accordingly
	if(ellipseXPos > width - ellipseRadius/2) {
	xVel = xVel*-1;	
	}
	
	if (ellipseXPos < ellipseRadius/2) {
	xVel = xVel*-1;	
	}
	
	//when touch top and bottom, changes speed accordingly
	if(ellipseYPos > height - ellipseRadius/2) {
	yVel = yVel*-1;	
	}
	
	if (ellipseYPos < ellipseRadius/2) {
	yVel = yVel*-1;	
	}
		
		
if (rectRightEdge > width/2 - 25 && rectRightEdge < width/2+25) {
	if (xVel > 0) {
	xVel *=-1;
	}
}
		
if (rectLeftEdge < width/2 + 25 && rectLeftEdge > width/2-25) {
	if (xVel < 0) {
	xVel *=-1;
	}
}
		
		
		
		
		
	rectMode(CENTER);
	fill(r, g, b);
  r = abs(xVel*5+yVel*5);	
	g = abs(xVel*5+yVel*5);	
	b = abs(xVel*5+yVel*5);	
	rect (0, 0,80, 80); 

	
	
	if (mousePressed) {
		if (xVel < 0.3 && yVel <0.3) {
		xVel = mouseX/10-ellipseXPos/10;
		yVel = mouseY/10-ellipseYPos/10;
		//	xVel *= -1;
		//yVel *= -1;
	//	print(xVel);
}
	}
	} //if size == 1
}

I know that my code also checks for areas that are unnecessary to check but I can’t figure out how i can do it without that line.
Sometimes the collision is of and mty rect can travel through it.

my code:
if (rectRightEdge > width/2 - 25 && rectRightEdge < width/2+25) {
if (xVel > 0) {
xVel *=-1;
}
}

if (rectLeftEdge < width/2 + 25 && rectLeftEdge > width/2-25) {
if (xVel < 0) {
xVel *=-1;
}
}

2

helps if you draw out the steps you need to code

image

unless you need to include rotations its essentially a four point to rect test.