Final answer:
To find the vertical distance between the points (12, -1) and (12, 7), the correct equation is d = |y2 - y1|, which results in d = |7 - (-1)| = 8. The vertical distance and displacement are both 8 units.
Step-by-step explanation:
The student is asking for the equation to find the vertical distance between two points on a coordinate plane. The correct equation for this situation is the absolute difference between the y-coordinates of the points since the x-coordinates are the same. So, for the points (12, -1) and (12, 7), the vertical distance is calculated as the absolute value of the difference between 7 and -1, which is |7 - (-1)|.
The correct equation to use is therefore d = |y2 - y1|, which in this case is d = |7 - (-1)| = |7 + 1| = |8| = 8. Thus, the vertical distance between the two points is 8 units. Displacement in a vertical line with the same start and end x-coordinates would be equal to the distance and also positive, so the displacement is also 8 meters.