Answer:
17 units
Explanation:
You want to know the distance from (-4, 7) to (-4, -10).
Distance
You can find the distance between two points using the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
For the given points, the distance is ...
d = √((-10 -7)² +(-4 -(-4))²) = √((-17)² +0²) = √289 = 17
The distance between the two points is 17 units.
__
Additional comments
The distance formula makes use of the positive square root, so it will always give a positive result.
"Distance" and "displacement" are different. "Distance" and "length" are always positive.
"Displacement" is measured relative to a reference point, with a positive direction defined. Negative displacements will be in the opposite direction from positive displacements.
The point (-4, -10) is to the left of the point (-4, 7) on the horizontal line y=-4. Its displacement from (-4, 7) is -17 units, but its distance from (-4, 7) is 17 units.
You may have noticed that the distance formula computed ...
√(-17)² = 17
It will be generally true that ...
√(x²) = |x|
The square root symbol always indicates the positive square root. That is why we use ±√( ) when we want to consider both possible square roots.