ramyaravindran wrote:Need help with this question
A line connects points A (1,1) and B (100,1000). How many other points with integer coordinates are on the line between A and B?
A. 0 B. 2 C. 3 D. 8 E. 9
Answer is D
Slope = (1000-1)/(100-1) = 999/99.
To make the math easier, SHIFT the line so that it passes through the origin.
Problem rephrased:
A line connects points A (0,0) and B (99,999). How many other points with integer coordinates are on the line between A and B?
The answer will be the same because the line that connects (0,0) and (99,999) has the SAME SLOPE as that in the original problem, points A and B still have INTEGER coordinates, and the DISTANCE between A and B is unchanged.
In the rephrased problem:
Slope = (999-0)/(99-0) = 999/99 = 111/11.
Since the y-intercept is 0, the equation of the line is as follows:
y = (111/11)x.
For y to be an integer, x must be a multiple of 11.
Since x=0 yields y=0 (the coordinates of point A), and x=99 yields y=999 (the coordinates of point B), x can be any multiple of 11 BETWEEN 0 and 99:
11, 22, 33, 44, 55, 66, 77, 88.
Total options = 8.
The correct answer is
D.
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