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Math Expert V
Joined: 02 Sep 2009
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In a rectangular coordinate system, if a line passes through the point  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 72% (01:36) correct 28% (01:59) wrong based on 25 sessions

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In a rectangular coordinate system, if a line passes through the points (-10,-18), (20,22) and (x,2) then what is the value of x?

A) 2
B) 3
C) 4
D) 5
E) 6

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Joined: 11 Sep 2015
Posts: 4604
GMAT 1: 770 Q49 V46
Re: In a rectangular coordinate system, if a line passes through the point  [#permalink]

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Bunuel wrote:
In a rectangular coordinate system, if a line passes through the points (-10,-18), (20,22) and (x,2) then what is the value of x?

A) 2
B) 3
C) 4
D) 5
E) 6

Key concept: If you take any portion of a particular line, the slope between ANY two points on the line will always be the same.

So, for example, the slope between points (-10, -18) and (20, 22) must be equal to the slope between points (20, 22) and (x, 2)

Slope between (-10, -18) and (20, 22)= (22 - (-18))/(20 - (-10)) = 40/30 = 4/3

This means the slope between points (20, 22) and (x, 2) must also equal 4/3

We can write: (2 - 22)/(x - 20) = 4/3
Simplify: -20/(x - 20) = 4/3
Multiply both sides by 3 to get: -60/(x - 20) = 4
Multiply both sides by (x - 20) to get: -60 = 4(x - 20)
Expand: -60 = 4x - 80
Solve: x = 5

Cheers,
Brent
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Re: In a rectangular coordinate system, if a line passes through the point  [#permalink]

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Bunuel wrote:
In a rectangular coordinate system, if a line passes through the points (-10,-18), (20,22) and (x,2) then what is the value of x?

A) 2
B) 3
C) 4
D) 5
E) 6

Using the two points with both known x- and y-coordinates, the slope of the line is:

[(22 - (-18)]/[20 - (-10)] = 40/30 = 4/3

Since the slope of the line is always the same, regardless of which points we use to determine it, we see that the slope between (x, 2) and (20, 22) should also be 4/3. Therefore, we can create the equation:

(22 - 2) / (20 - x) = 4/3

20 / (20 - x) = 4/3

60 = 80 - 4x

-20 = -4x

5 = x

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: In a rectangular coordinate system, if a line passes through the point   [#permalink] 08 Feb 2020, 12:22
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