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

Question

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

NandishSS · Answer

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

niks18 · Answer

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

Adi93 · Answer

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

dave13 · Answer

Hi NandishSS ,

why slope AB = 1/2 and not -1/2 ? -3-0/ 6-0 = -3/6

no ?

thanks!

NandishSS · Answer

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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