True or False? The points A(-1,-7), B(1,-1), and C(2,2) are collinear.?

TRUEEEEEEE i solved itTrue or False? The points A(-1,-7), B(1,-1), and C(2,2) are collinear.?
Points A(-1,-7), B(1,-1), and C(2,2) are collinear if they have same slope.


Let:


point A (x1 , y1)


point B (x2 , y2)


point C (x3 , y3)





m1 = (y2 - y1) / (x2 - x1)


m2 = (y3 - y2) / (x3 - x1)





m1 = m2





check





m1 = [-1 - (-7)] / [1 - (-1)] = 6 / 2 = 3


m2 = [(2 - (-1)] / (2 - 1) = 3 / 1 = 3





so m1 = m2


then all points are collinearTrue or False? The points A(-1,-7), B(1,-1), and C(2,2) are collinear.?
can never be true
Sure enough!
find the slope of AB


the slope = ( -1 + 7 ) / ( 1 + 1 ) = 6 / 2 = 3





find the slope of BC


the slope = ( 2 +1 ) / ( 2 - 1 ) = 3 / 1 = 3





then the slope of AB = the slope of BC


then A , B , C are collinear
True
Gradient of line AB is (-1+7)/(1+1) = 3


Gradient of line BC is (2+1)/(2-1) = 3


Hence A, B, C are points along a straight line and they are collinear.
false
no they are not


u can calculate the gradient of the lines betwen each consecutive point and u will see that the gradients are differnt thus the points r not colinear

ie