Find the number of points on the straight line between points (-4.11) to (16.-1) whose coordinates (both x and y coordinates are positive integer
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Answer:
The slope of the line is,
16−(−4)
−1−11
=
20
−12
=
5
−3
Thus, the eqn of the line is,
y−11=
5
−3
(x−(−4))=
5
−3
x
5
−12
=
5
−1
(3x+12)
y is am integer precisely when 3x+12 is a multiply of 5, which is when (x+4) is a multiple of 5
These values of x occur 5 units apast, between −4 and 6 they arn't −4,1,6,11 and 16 and corresponding y− coordinates are 11,8,5,2 and −1.
They values of x between −4 and 6 that give integral values of y must be −4,1,6,11 and 16. The corresponding y− coordinates are 11,8,5,2 and −1.
The line segment constants exactly 3 points whose coordinates are path positive integers.
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