all of the following are coordinates on the same straight line except:
A) (0,2)
B) (3,11)
C) (5,15)
D) (7,23)
E) (x,3x+2)
put a line through A and B
slope = 9/3 = 3
2 = 3 (0) + b
y = 3 x + 2
now c
15 = 3*5+2 no, oh dear
then D
23 = 3*7 + 2 yes
and E
3x+2 = 3 x + 2 yes
So C is no good, invalid, evil, boil in oil
Thanks Damon. Now I understand the concept of it.
You are welcome :)
To determine which coordinate points lie on the same straight line, we can use the concept of slope.
The slope of a line is given by the formula:
slope = (change in y-coordinates)/(change in x-coordinates)
For the given coordinates, let's calculate the slopes between each pair of points:
Slope between (0,2) and (3,11):
Slope = (11 - 2)/(3 - 0) = 9/3 = 3
Slope between (0,2) and (5,15):
Slope = (15 - 2)/(5 - 0) = 13/5
Slope between (0,2) and (7,23):
Slope = (23 - 2)/(7 - 0) = 21/7 = 3
For the given coordinates, the slope is not consistent except between (0,2) and (7,23), where the slope is 3. Therefore, the point that does not lie on the same straight line as the others is (5,15) [Option C].