Anyone know how to do this? (10)

The correct answer is:  [C]:  " (-5,-1) "  ;  " 2√6  units " .

Explanation:

Use the Pythagorean theorem:

5² + 1² = c²  ;

↔ c² = 5² − 1² ;

in which "c" = (magnitude of ray "PQ") ;

    c² = 25 − 1 = 24 ;

    c² = 24 ;


   +√(c²) = +√(24) ;

 
c = √(24) = √6 * √ 4 = √6 *2 = 2√6

  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)".

Consider that "M" is point: "(5,6)" → x = 5, y = 6.

Consider that "P"  is point: "(0,5") → x = 0, y = 5.

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)" .

    →  The correct answer is:  [C]:  " (-5,-1) "  ;  " 2√6  units " .