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
No clue how to proceed with this. Please help!
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prachi18oct
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Hi prachi18oct,
You might find it helpful to draw the two points and the line segment between them, but doing so is not necessary to get to the solution.
To figure out the number of integer points between point A and point B, we need to know the SLOPE of the line segment (from the answer choices, we know that there are from 4 to 15 integer points):
Slope = (Change in Y)/(Change in X) = Rise/Run
Point A = (5,7)
Point B = (10,-3)
Slope = (7 - (-3))/(5-10) = 10/-5 = -2
Since the slope is - 2, for every 1 we "move to the right", we move "down" 2.... we can now 'map out' the various integer co-ordinates between Point A and Point B:
Point A = (5,7)
(6, 5)
(7, 3)
(8, 1)
(9, -1)
Point B = (10, -3)
Since the question asks for the number of points BETWEEN A and B, the answer is 4.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
You might find it helpful to draw the two points and the line segment between them, but doing so is not necessary to get to the solution.
To figure out the number of integer points between point A and point B, we need to know the SLOPE of the line segment (from the answer choices, we know that there are from 4 to 15 integer points):
Slope = (Change in Y)/(Change in X) = Rise/Run
Point A = (5,7)
Point B = (10,-3)
Slope = (7 - (-3))/(5-10) = 10/-5 = -2
Since the slope is - 2, for every 1 we "move to the right", we move "down" 2.... we can now 'map out' the various integer co-ordinates between Point A and Point B:
Point A = (5,7)
(6, 5)
(7, 3)
(8, 1)
(9, -1)
Point B = (10, -3)
Since the question asks for the number of points BETWEEN A and B, the answer is 4.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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prachi18oct
- Master | Next Rank: 500 Posts
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Can you explain the bolded part in detail.[email protected] wrote:Hi prachi18oct,
Slope = (7 - (-3))/(5-10) = 10/-5 = -2
Since the slope is - 2, for every 1 we "move to the right", we move "down" 2.... we can now 'map out' the various integer co-ordinates between Point A and Point B:
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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Slope = (y₂ - y�)/(x₂ - x�) = (-3-7)/(10-5) = -10/5 = -2.prachi18oct 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
Thus, the equation of the line is as follows:
y = -2x + b.
To determine the value of b, plug (x, y) = (5,7) into y = -2x + b and solve for b:
7 = -2*5 + b
b = 17.
Thus, the equation of the line is as follows:
y = -2x + 17.
Since A = (5, 7) and B = (10, -3), any point BETWEEN A AND B must have an x-coordinate BETWEEN 5 AND 10.
Between 5 and 10 there are four integer options for x:
6, 7, 8 and 9.
Plug x=6, x=7, x=8 and x=9 into y = -2x + 17.
If x=6, then y = -2x + 17 = -2*6 + 17 = 5.
If x=7, then y = -2x + 17 = -2*7 + 17 = 3.
If x=8, then y = -2x + 17 = -2*8 + 17 = 1.
If x=9, then y = -2x + 17 = -2*9 + 17 = -1.
Thus, four points between A and B have coordinates that are integer values:
(6, 5)
(7, 3)
(8, 1)
(9, -1).
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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