Although you can draw an infinite number of lines through the midpoint of a segment, you can draw only one line that is to the line segment.

Perpendicular

Step-by-step explanation: Took the quiz :)

  b: elimination

Step-by-step explanation:

My vote is for elimination, though any of these methods (and some not listed) will get an answer quickly.

Subtracting the second equation from twice the first gives ...

  2(9x +8y) -(18x -15y) = 2(7) -(14)

  31y = 0 . . . simplify

  y = 0 . . . . . divide by 31 (or invoke the zero-product rule)

Then the value of x can be found from the first equation:

  9x = 7

  x = 7/9

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I like this method because it tells you that y=0 in one step. (Graphing does the same.) For the numbers here, you can do it mentally. Once you recognize that the x-coefficients and the constants are related by the same factor, and that factor is different for the y-coefficients, it becomes apparent that elimination will immediately tell you that y=0.