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In a rectangular coordinate system, which of the following p

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In a rectangular coordinate system, which of the following p [#permalink] New post 29 Jul 2020, 10:51
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In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5,6) and (21,18)?

A. (9,9)
B. (12,12)
C. (13,13)
D. (12,13)
E. (16,15)


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[Reveal] Spoiler: OA

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Re: In a rectangular coordinate system, which of the following p [#permalink] New post 29 Jul 2020, 11:06
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Carcass wrote:
In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5,6) and (21,18)?

A. (9,9)
B. (12,12)
C. (13,13)
D. (12,13)
E. (16,15)


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One approach is to first find the slope
Slope = (18 - 6)/(21 - 5) = 12/16 = 3/4

IMPORTANT: if the slope is 3/4, then we can start at (5,6) and move up 3 spaces and then move right 4 spaces to find other points on the line (with INTEGER values)

Start at: (5,6)
Move 3 units up and 4 units to the right to get to the point (9,9) (check answer choices - it's there!)

Answer: A

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Brent
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Re: In a rectangular coordinate system, which of the following p [#permalink] New post 29 Jul 2020, 11:30
Equation of line passing from (5,6) and (21,18) can be written as

(y - 6)/(x - 5) = (18 - 6)/(21 - 5) = 12/16 = 3/4
=> 4y - 24 = 3x - 15
=> 4y = 3x + 9

Option A (9,9) satisfies this equation.

So, the answer is A.
Re: In a rectangular coordinate system, which of the following p   [#permalink] 29 Jul 2020, 11:30
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In a rectangular coordinate system, which of the following p

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