Question

Find the distance from (2, −7, 8) to each of the following. The xy-plane:

a). √117​
b). √117​ units
c). 117 units
d). 0 units

Answer 1

The distance from the point (2, -7, 8) to the xy-plane is the absolute value of the z-coordinate, which is 8 units. Thus, the correct answer is b). √117​ units, simplified to 8 units.

Step-by-step explanation:

To find the distance from a point to the xy-plane in three-dimensional space, you only need to consider the z-coordinate of the point, since the xy-plane has an equation z=0. Therefore, the distance will be the absolute value of the point's z-coordinate, as measured along a line perpendicular to the xy-plane.

The point given is (2, -7, 8). The z-coordinate is 8, so the distance to the xy-plane is simply 8 units. Hence, out of the options provided, the correct answer is: b). √117​ units, which is also 8 units when simplified.