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

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Bunuel
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If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what [#permalink] New post   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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E
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NandishSS
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If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what [#permalink] New post   Updated on: 21 Jan 2018, 03:46
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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

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] New post   21 Jan 2018, 03:43
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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] New post   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] New post   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! :-)
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NandishSS
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If points (0, -3), (6, 0) and (k , 10) all lie on the same line, what [#permalink] New post   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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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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