Which of the following coordinates are on the line segment connecting (5, 6) and (21, 18)?  Choose one.
A) (9, 9)  B) (12, 12)  C) (13, 13)  D) (12, 13)  E) (16, 15)
The line segment connects (5,6) to (21,18), therefore the change in the x-coordinate is 16, and the change in the y-coordinate is 12. We can simplify that to a slope of 3/4. That is, the points on the line with integer coordinates will all be of the form (5+4n, 6+3n). Put simply, starting at the point (5,6), to find the next point with integer coordinates on the line, all we have to do is add 4 to the x-coordinate and 3 to the y-coordinate. Then we can continue to do that until we find one of the answer choices.   In this case, the next point would be (5+4, 6+3), or (9,9). That is one of the answer choices, so the answer is A.   If (9,9) wasn't an option we could continue to add 4 to the x-coordinate and 3 to the y-coordinate until we found a point that was in the answer choices. The points are:   (5,6)   (9,9)   (13,12)   (17,15)   (21,18)   Beyond that and we are no longer on the line segment connecting the two original points.   (9, 9)nswer: (9, 9)
<result>A</result>
Which of the following coordinates are on the line segment connecting (5, 6) and (21, 18)?