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A rectangle, with its vertex coordinates labeled, is graphed in the standard (x,y) coordinate plane below. A lattice point is a point with coordinates that are both integers. A lattice point inside but NOT on the rectangle will be chosen at random. What is the probability that the sum of the x-coordinate and the y-coordinate of the chosen lattice point will be odd

User Not An ID
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The probability that the sum of the x-coordinate and the y-coordinate of the chosen lattice point will be odd is 7/15. The correct answer is 7/15.

The image shows a rectangle with vertices at (0,0), (6,0), (6,4), and (0,4). The lattice points inside the rectangle are:

(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3)

There are 15 lattice points inside the rectangle.

Of these, 7 have an odd sum:

(1,1), (1,3), (2,1), (2,3), (3,1), (3,3), (5,1).

Therefore, the probability that the sum of the x-coordinate and the y-coordinate of the chosen lattice point will be odd is 7/15.

The correct answer is 7/15.

Question

A Rectangle, with its vertex coordinates labeled, s graphed in the standard coordinate plane below. A lattice point is a point with coordinates that are both integers. A lattice point inside but not on the rectangle will be chosen at random. What is the probability that the sum of the x-coordinate d the y coordinate of the chose lattice point will be odd?

- 1/5

- 2/5

- 7/15

- 17/35

- 1/2

A rectangle, with its vertex coordinates labeled, is graphed in the standard (x,y-example-1
User Kanimbla
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