Final answer:
To find the distance from a point to each of the given options, use the distance formula.
Step-by-step explanation:
To find the distance from (-1,7,-10) to each of the given points, we can use the distance formula. The distance formula is √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2). Substituting the coordinates of the given point and each of the options into the formula will give us the distance.
a. Distance = √((-1-(-1))^2 + (7-7)^2 + (-10-(-10))^2) = √((0)^2 + (0)^2 + (0)^2) = 0 km
b. Distance = √((-1-(-1))^2 + (7-7)^2 + (-10-0)^2) = √((0)^2 + (0)^2 + (-10)^2) = 10 km
c. Distance = √((-1-7)^2 + (7-7)^2 + (-10-0)^2) = √((-8)^2 + (0)^2 + (-10)^2) = √(64 + 0 + 100) = √164 km
d. Distance = √((-1-7)^2 + (7-7)^2 + (-10-0)^2) = √((-8)^2 + (0)^2 + (-10)^2) = √(64 + 0 + 100) = √164 km