Answer:
B: (0, -4)
Step-by-step explanation:
Three points are collinear if they lie on a single straight line. As we know two points of the line, there is a unique line that passes through both of them.
Let's find the equation of the line:
The general equation of a line is y = mx + b, where m represents the slope and b is the y-intercept.
In this case, we know that
[tex]\left \{ {{6 = m*3 + b} \atop {-9 = m*(-2) + b}} \right. \\[/tex]
because we want the line to passes through (3, 6) and (-2, -9)
From the first equation, we deduce that [tex]b = 6 - m*3[/tex]
We replace this in the second one and we get
[tex]-9 = (-2)*m + 6 - 3*m\\ -15 = (-5)*m [/tex]
3 = m
With this, b = 6 - 3*m = 6 - 3*3 = -3
b = -3
So, the equation of the line that passes through (3, 6) and (-2, -9) is
[tex]\fbox {y = 3x - 3}[/tex]
Knowing these, let's see which one of A, B, C or D makes the equation false, i.e. doesn't lie on the line and therefore is not collinear with (3, 6) and (-2, -9). For that, in each case, we have to replace the x of the equation with the first number of the pair and see if it equals the second one.
A: 3*(-1) - 3 = -3 -3 = -6. Correct!
B: 3*0 - 3 = 0 - 3 = -3. Wrong!
C: 3*3 - 3 = 9 - 3 = 6. Correct!
D: 3*0 - 3 = 0 - 3 = -3. Correct!
Therefore, B is not collinear with (3, 6) and (-2, -9)
