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Home » 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.
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.
CBSE | Class 11 | Exercise 28.1 | Introduction to Three Dimensional Coordinate Geometry | Maths | RD Sharma
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.

Given: 

Point

    \[\left( 3,\text{ }-2,\text{ }5 \right)\]

The Absolute value of any point

    \[\left( x,\text{ }y,\text{ }z \right)\]

is given by,

    \[\surd ({{x}^{2}}~+\text{ }{{y}^{2}}~+\text{ }{{z}^{2}})\]

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

So let the point

    \[A\left( 3,\text{ }-2,\text{ }5 \right)\]

Remaining

    \[7\]

points are:

    \[Point\text{ }B\left( 3,\text{ }2,\text{ }5 \right)\]

(By changing the sign of y coordinate)

    \[Point\text{ }C\left( -3,\text{ }-2,\text{ }5 \right)\]

(By changing the sign of x coordinate)

    \[Point\text{ }D\left( 3,\text{ }-2,\text{ }-5 \right)\]

(By changing the sign of z coordinate)

    \[Point\text{ }E\left( -3,\text{ }2,\text{ }5 \right)\]

(By changing the sign of x and y coordinate)

    \[Point\text{ }F\left( 3,\text{ }2,\text{ }-5 \right)\]

(By changing the sign of y and z coordinate)

    \[Point\text{ }G\left( -3,\text{ }-2,\text{ }-5 \right)\]

(By changing the sign of x and z coordinate)

    \[Point\text{ }H\left( -3,\text{ }2,\text{ }-5 \right)\]

(By changing the sign of x, y and z coordinate)

i

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