Pygame make sprite walk in given rotation

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Detect when the mouse is clicked with the MOUSEBUTTONDOWN event:

if event.type == pygame.MOUSEBUTTONDOWN:
    mouse_x, mouse_y = event.pos

Compute the vector from the center of the sprite to the mouse click position:

dx = mouse_x - star.rect.centerx
dy = mouse_y - star.rect.centery

Compute the length of the vector (Euclidean distance):

dist = math.sqrt(dx*dx + dy*dy)

or

dist = math.hypot(dx, dy)

Normalize the vector (Unit vector). A normalized vector has a length of 1:

if dist > 0:
    dx /= dist
    dy /= dist

Move the object a certain number of steps in the direction of the vector:

star.rect.x += steps * dx
star.rect.y += steps * dy

See also Follow target or mouse

Minimal example:

import pygame, random, math

class Star(pygame.sprite.Sprite):
    def __init__(self):
        super().__init__()
        self.image = img_star
        self.rect = self.image.get_rect()
        self.velocity = [0, 0]
        self.rect.x = random.randint(0, window_x)
        self.rect.y = random.randint(0, window_y)

pygame.init()
window_x, window_y = 500, 500
window = pygame.display.set_mode((window_x, window_y))
clock = pygame.time.Clock()

img_star = pygame.Surface((20, 20), pygame.SRCALPHA)
pygame.draw.circle(img_star, (255, 255, 0), (10, 10), 10)
star = Star()
group = pygame.sprite.Group(star)

run = True
while run:
    clock.tick(60)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False          
        if event.type == pygame.MOUSEBUTTONDOWN:
            mouse_x, mouse_y = event.pos
            dx = mouse_x - star.rect.centerx
            dy = mouse_y - star.rect.centery
            dist = math.sqrt(dx*dx + dy*dy)
            steps = 10
            if dist > 0:
                star.rect.x += steps * dx / dist
                star.rect.y += steps * dy / dist

    window.fill(0)
    group.draw(window)
    pygame.display.flip()

pygame.quit()
exit()

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