ccassel wrote:Hi,
What steps would you take to solve this question?
In a rectangular coordinate system, triangle P (0, 30) , O (0, 0), Q (50, 0) lie on the grid, how many of the points on line segment PQ have coordinates that are both integers?
A. 5
B. 8
C. 10
D. 11
E. 20
Cheers,
The slope of line segment PQ is -3/5.
The y intercept is 30.
Thus, the equation of the line is y = (-3/5)x + 30.
Multiplying the equation by 5, we get:
5y = -3x + 150
3x + 5y = 150.
We need to determine how many non-negative integer values for (x,y) work in the equation above.
The smallest possible value of x is 0.
Since 3*50 = 150, the largest possible value of x is 50.
If x is a multiple of 5, then y will be an integer.
Multiples of 5 between 0 and 50, inclusive = 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 = 11 values.
The correct answer is
D.
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