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If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what

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If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what  [#permalink]

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21 Jan 2018, 03:33
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If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what is the value of k ?

(A) 2
(B) 8
(C) 14
(D) 22
(E) 26

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Posts: 689
Location: India
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If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what  [#permalink]

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Updated on: 21 Jan 2018, 03:46
1
Bunuel wrote:
If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what is the value of k ?

(A) 2
(B) 8
(C) 14
(D) 22
(E) 26

If points A(0, -3), B(6, 0) and C(k , 10) all lie on the same line

Slope =y2-y1/x2-x1

Slope of AB= Slope of BC

Slope of AB = 1/2

Slope BC = 1/2 =10/(k-6)

K=26

Hence E
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Originally posted by NandishSS on 21 Jan 2018, 03:41.
Last edited by NandishSS on 21 Jan 2018, 03:46, edited 1 time in total.
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If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what  [#permalink]

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21 Jan 2018, 03:43
1
Bunuel wrote:
If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what is the value of k ?

(A) 2
(B) 8
(C) 14
(D) 22
(E) 26

Another approach can be to find the equation of the line

using points (0,-3) & (6,0) we can find the equation of the line

so we have $$y=\frac{(y_1-y_2)}{(x_1-x_2)}*x+c$$

$$=>y=\frac{-3-0}{0-6}*x+c$$

$$=>2y=x+2c$$, Now to get the value of $$2c$$, we can use points (6,0)

$$=>0=6+2c=>2c=-6$$

so equation of the line is $$2y=x-6$$

hence at (k,10) we have $$2*10=k-6$$

$$=>k=26$$

Option E
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If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what  [#permalink]

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21 Jan 2018, 05:41
Bunuel wrote:
If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what is the value of k ?

(A) 2
(B) 8
(C) 14
(D) 22
(E) 26

When the 3 points lie on the same line.Area formed by 3 points is 0.
1/2 det|0 -3 1 |
|6 0 1 |
|k 10 1|
18-3k+60=0
k=26
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Re: If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what  [#permalink]

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21 Jan 2018, 07:49
NandishSS wrote:
Bunuel wrote:
If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what is the value of k ?

(A) 2
(B) 8
(C) 14
(D) 22
(E) 26

If points A(0, -3), B(6, 0) and C(k , 10) all lie on the same line

Slope =y2-y1/x2-x1

Slope of AB= Slope of BC

Slope of AB = 1/2

Slope BC = 1/2 =10/(k-6)

K=26

Hence E

Hi NandishSS,

why slope AB = 1/2 and not -1/2 ?

-3-0/ 6-0 = -3/6 no ?

thanks!
Director
Joined: 06 Jan 2015
Posts: 689
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what  [#permalink]

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21 Jan 2018, 19:05
dave13 wrote:
NandishSS wrote:
Bunuel wrote:
If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what is the value of k ?

(A) 2
(B) 8
(C) 14
(D) 22
(E) 26

If points A(0, -3), B(6, 0) and C(k , 10) all lie on the same line

Slope =y2-y1/x2-x1

Slope of AB= Slope of BC

Slope of AB = 1/2

Slope BC = 1/2 =10/(k-6)

K=26

Hence E

Hi NandishSS,

why slope AB = 1/2 and not -1/2 ?

-3-0/ 6-0 = -3/6 no ?

thanks!

HI dave13,

x1=0 y1= -3 x2=6, y2=0

Slope =(y2-y1)/(x2-x1) OR Slope =(y1-y2)/(x1-x2)

Both are correct, here 0-(-3)/(6-0)= 1/2

I hope it is clear now
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Resource: GMATPrep RCs With Solution
If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what   [#permalink] 21 Jan 2018, 19:05
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