Question

The coordinates of a point are (3, -2, 5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point.

Answer 1

Given: Point (3, -2, 5) 

To find: the coordinates of 7 more points such that the absolute values of all 8 coordinates are the same 

Formula used: Absolute value of any point(x, y, z) is given by,

\(\sqrt{x^2+y^2+z^2}\)

We need to make sure that absolute value to be the same for all points 

In the formula of absolute value, there is square of the coordinates. So when we change the sign of any of the coordinates, it will not affect the absolute value. 

Let point A(3, -2, 5) 

Remaining 7 points are: 

Point B(3, 2, 5) (By changing the sign of y coordinate) 

Point C(-3, -2, 5) (By changing the sign of x coordinate) 

Point D(3, -2, -5) (By changing the sign of z coordinate) 

Point E(-3, 2, 5) (By changing the sign of x and y coordinate) 

Point F(3, 2, -5) (By changing the sign of y and z coordinate) 

Point G(-3, -2, -5) (By changing the sign of x and z coordinate) 

Point H(-3, 2, -5) (By changing the sign of x, y and z coordinate)