The correct answer is: [C]: " (-5,-1) " ; " 2√6 units " .
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Explanation:
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Use the Pythagorean theorem:
5² + 1² = c² ;
↔ c² = 5² − 1² ;
in which "c" = (magnitude of ray "PQ") ;
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c² = 25 − 1 = 24 ;
c² = 24 ;
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+√(c²) = +√(24) ;
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c = √(24) = √6 * √ 4 = √6 *2 = 2√6
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Now, since we now, that "c", or the magnitude of "ray MP", is: "2√6" ; we can consider the answer choices given, and can narrow our options
to choices: A or D. The first part of the question asks us to find the ordered pair that represents "ray MP". From choices: A or D, we have: (-1, -5) ; and (-5, -1) ; respectively. Note that these ordered pairs are written as: "(x, y)".
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Consider that "M" is point: "(5,6)" → x = 5, y = 6.
Consider that "P" is point: "(0,5") → x = 0, y = 5.
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From "M" to "P" , we go from "x = 5" ; to: "x = 0".
That is a DECREASE of 5 units in the x-value; so, x = -5.
From "M" to "P", we go from "y = 6" ; to "y = 5".
That is a decrease of "1" in the "y-value; so, y = -1.
Thus, the ordered pair that represents the "ray MP" is: "(-5, -1)" .
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→ The correct answer is: [C]: " (-5,-1) " ; " 2√6 units " .
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