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# How many integer points lie between points A and B on the line segment

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
How many integer points lie between points A and B on the line segment  [#permalink]

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17 Sep 2018, 21:10
00:00

Difficulty:

55% (hard)

Question Stats:

39% (01:03) correct 61% (02:09) wrong based on 18 sessions

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How many integer points lie between points A and B on the line segment AB, if A is (5, 7) and B is (10, -3)?

A. 4
B. 5
C. 6
D. 10
E. 15

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Re: How many integer points lie between points A and B on the line segment  [#permalink]

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18 Sep 2018, 00:20
Bunuel wrote:
How many integer points lie between points A and B on the line segment AB, if A is (5, 7) and B is (10, -3)?

A. 4
B. 5
C. 6
D. 10
E. 15

Slope of line passing through (5, 7) and (10, -3) = [7-(-3)]/[5-10] = -2

i.e. y = -2x +c
Since point (5,7) satisfies the equation hence

(7) = -2*(5) +c
i.e. c = 17

i.e. Equation of line becomes y = -2x +17

Now teh value of x may be taken as 6, 7, 8 and 9 for the points to lie between A and B hence there are only 4 more points because for each integer value fo x, y will be Integer as well as per the equation obtained. hence

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Re: How many integer points lie between points A and B on the line segment &nbs [#permalink] 18 Sep 2018, 00:20
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# How many integer points lie between points A and B on the line segment

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