Answer:
[tex]\mathrm{Solution\:} = (- 7,7) = \mathrm{Last\:}\mathrm{Option\:}[/tex]
Step-by-step explanation:
In my point of view the easiest approach to solving this problem would be by determining the distance between the given points (the midpoint and the other given point) --- (1) and then going through all the answer choices and matching their distance to the midpoint --- (2). This may seem like a hard approach, but you can eliminate many of the answer choices.
The answer is the last choice, so let's prove it.
[tex]\mathrm{Distance\:between\:}\left(1,\:5\right)\mathrm{\:and\:}\left(9,\:3\right) = \sqrt{\left(9-1\right)^2+\left(3-5\right)^2} = 2\sqrt{17}[/tex]
[tex]\mathrm{Distance\:between\:}\left(1,\:5\right)\mathrm{\:and\:}\left(-7,\:7\right)=\sqrt{\left(-7-1\right)^2+\left(7-5\right)^2}=2\sqrt{17}[/tex]
[tex]2\sqrt{17} = 2\sqrt{17}[/tex]
As the distance between points (1,5) and (9,3) respectively (1,5) and (- 7,7) is the same, we proved that our answer is the last choice.
