Answer: Choice C. (2,6) and (-4,-7)
=========================================================
Step-by-step explanation:
The original line has a given slope of -6/13. The opposite reciprocal is 13/6. We flip the fraction and the sign from negative to positive.
With any two perpendicular slopes, they always multiply to -1
(-6/13)*(13/6) = (-6*13)/(13*6) = -78/78 = -1
--------------------
Since the perpendicular slope is 13/6, we need to see which of the four answer choices produces a slope of 13/6. Use the slope formula.
This is something you do through trial and error. You could start with A and work your way to D, or just pick at random. I'll go through each one by one starting at choice A.
---------------------
Let's try choice A
m = (y2 - y1)/(x2 - x1)
m = (2 - (-4))/(-7 - 13)
m = (2 + 4)/(-7 - 13)
m = 6/(-20)
m = -3/10, we can see that choice A is not the answer, since we want m = 13/6 instead.
-----------------------
Let's try choice B
m = (y2 - y1)/(x2 - x1)
m = (2 - (-4))/(-7 - 6)
m = (2 + 4)/(-7 - 6)
m = 6/(-13)
m = -6/13, that doesn't work either
------------------------
Let's try choice C
m = (y2 - y1)/(x2 - x1)
m = (-7 - 6)/(-4 - 2)
m = -13/(-6)
m = 13/6, we found the answer
------------------------
For the sake of completeness, here is what choice D would look like
m = (y2 - y1)/(x2 - x1)
m = (-4 - 9)/(-4 - 6)
m = -13/(-10)
m = 13/10, which isn't the slope we want