Question

Calculate the distances from the origin to points A(11, –2, –6) and B(–3, 7, –5). Round to the nearest tenth. The distance from the origin to point A is units. The distance from the origin to point B is units. Now determine how much farther from the origin point A is than point B. Round to the nearest tenth. Point A is units farther from the origin than point B.

Answer 1

The distance from the origin to point A is 12.7 units.

The distance from the origin to point B is 9.1 units.

Point A is 3.6 units farther from the origin than point B.

Answer 2

Explanation:

A(11, –2, –6) and B(–3, 7, –5) are located away from the origin (0,0,0), the points from the origin to this points is expressed as OB - OA where;

OB is the distance from the origin to the point B

OA is the distance from the origin to the point A

Using the formula for calculating distance between two points

OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²

OA = √(-6-0)²+(-2-0)²+(11-0)²

OA = √(-6)²+(-2)²+(11)²

OA = √36+4+121

OA = √161

OA = 12.688

Similarly;

OB = √(-5-0)²+(7-0)²+(-3-0)²

OA = √(-5)²+(7)²+(-3)²

OA = √25+49+9

OA = √83

OA = 9.110

Distance from the origin to the points = 12.688 - 9.110 = 3.577

Distance from the origin to the points ≈ 3.6 (to the nearest tenth)