What is the distance between points p(10, 7) and q(1, 8)?

If you plot those two points, draw the segment that connects them, then draw lines down and across from each point so they intersect, you'll create 2 right triangles. 

The hight will be the difference in the y's of the points, and the length will be the difference of the x's of the points. 

Using pythagorean theorm, you can then find the length of the hypotenuse, the segment connecting the points. 

P(10, 7) and Q(1, 8) 

change in y: 7 - 8 = -1 
change in x: 10 - 1 = 9 

Pythagorean theorm takes care of that negative since it squares both numbers, so I'll ignore that for now. we have: 

1² + 9² = c² 
1 + 91 = c² 
c² = 92 
c = 2√23 

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#2 is a horizontal line due to no change in y. subtract your x's. 

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The right answer is option d.