Find the Standard Equation of a Sphere That Has Diameter $( 3 , - 2,4 ) , ( 7,12,4 )$

question 80

Multiple Choice

Find the standard equation of a sphere that has diameter with the end points given below. $( 3 , - 2,4 ) , ( 7,12,4 )$

• A) \(( x - 5 ) ^ { 2 } + ( y - 5 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 53\)
• B) \(( x - 5 ) ^ { 2 } + ( y - 5 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 9\)
• C) \(( x + 5 ) ^ { 2 } + ( y - 5 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 53\)
• D) \(( x - 5 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z + 4 ) ^ { 2 } = 53\)
• E) \(( x - 5 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 53\)

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Definitions:

Postconventional Reasoning

The highest stage in Kohlberg's theory of moral development, characterized by the ability to think abstractly and make decisions based on universal ethical principles rather than concrete rules or expectations.

Sensorimotor Stage

The first stage of Piaget's theory of cognitive development, occurring from birth to about 2 years of age, where infants learn about the world through their senses and motor activities.

Formal Operational

The stage in Piaget's theory of cognitive development where individuals gain the ability to think abstractly, reason logically, and understand hypothetical concepts.

Preoperational

A stage in Piaget's theory of cognitive development where children from 2 to 7 years old engage in symbolic play and struggle with logic.