Step 1: Get the initial coordinates of point M, which is (6, 3).
Step 2: The point M is shifted left by 2 units. To represent the leftward motion, we subtract the distance from the x-coordinate of point M. So, we calculate the new x-coordinate like this: 6 - 2 = 4.
Step 3: Then, the point M is moved down by 7 units. To represent this downward motion, we subtract the distance from the y-coordinate of point M. So, we calculate the new y-coordinate like this: 3 - 7 = -4.
Step 4: Combining the new x and y coordinates, we get the translated point M' which is (4, -4). So, point M' which is the result of translating point M 2 units left and 7 units down is at position (4, -4).