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Subject Test Math 2

Question 1 of 28

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SAT Subject Test

What is the distance in space between the points with coordinates left parenthesis negative 3 comma 6 comma 7 right parenthesis and left parenthesis 2 comma negative 1 comma 4 right parenthesis?

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4.36

Correct Answer: 
No

5.92

Correct Answer: 
No

7.91

Correct Answer: 
No

9.11

Correct Answer: 
Yes

22.25

Correct Answer: 
No

The correct answer is D.

The distance d between the points with coordinates left parenthesis x subscript 1 end subscript comma y subscript 1 end subscript comma z subscript 1 end subscript right parenthesis and left parenthesis x subscript 2 end subscript comma y subscript 2 end subscript comma z subscript 2 end subscript right parenthesis is given by the distance formula: d equals square root of left parenthesis x subscript 2 end subscript minus x subscript 1 end subscript right parenthesis to the power of 2 end exponent plus left parenthesis y subscript 2 end subscript minus y subscript 1 end subscript right parenthesis to the power of 2 end exponent plus left parenthesis z subscript 2 end subscript minus z subscript 1 end subscript right parenthesis to the power of 2 end exponent end root.

Therefore, the distance between the points with coordinates left parenthesis negative 3 comma 6 comma 7 right parenthesis and left parenthesis 2 comma negative 1 comma 4 right parenthesis is: 
square root of left parenthesis 2 minus left parenthesis negative 3 right parenthesis right parenthesis to the power of 2 end exponent plus left parenthesis negative 1 minus 6 right parenthesis to the power of 2 end exponent plus left parenthesis 4 minus 7 right parenthesis to the power of 2 end exponent end root equals square root of 5 to the power of 2 end exponent plus left parenthesis negative 7 right parenthesis to the power of 2 end exponent plus left parenthesis negative 3 right parenthesis to the power of 2 end exponent end root equals square root of 25 plus 49 plus 9 end root which simplifies to square root of 83 end root almost equal to 9.11.

Question Difficulty: 
easy