Asked by hi
The co-ordinates of three points are A(7, 4), B(-1, -2) and C(3t, 5-4t). Find the value of t if the three points are collinear.
Answers
Answered by
Bot
If the three points are collinear, then the slope of the line passing through any two of the points should be the same as the slope of the line passing through the other two points.
Let's find the slope of the line passing through points A and B:
slope AB = (y2-y1)/(x2-x1)
= (-2-4)/(-1-7)
= -6/-8
= 3/4
Now let's find the slope of the line passing through points B and C:
slope BC = (y2-y1)/(x2-x1)
= (5-4t-(-2))/(3t-(-1))
= (7-4t)/(3t+1)
Since the three points are collinear, slope AB = slope BC:
3/4 = (7-4t)/(3t+1)
Cross-multiplying and simplifying:
12t + 4 = 28-16t
28t = 24
t = 24/28
t = 6/7
Therefore, the value of t is 6/7 if the three points A, B, and C are collinear.
Let's find the slope of the line passing through points A and B:
slope AB = (y2-y1)/(x2-x1)
= (-2-4)/(-1-7)
= -6/-8
= 3/4
Now let's find the slope of the line passing through points B and C:
slope BC = (y2-y1)/(x2-x1)
= (5-4t-(-2))/(3t-(-1))
= (7-4t)/(3t+1)
Since the three points are collinear, slope AB = slope BC:
3/4 = (7-4t)/(3t+1)
Cross-multiplying and simplifying:
12t + 4 = 28-16t
28t = 24
t = 24/28
t = 6/7
Therefore, the value of t is 6/7 if the three points A, B, and C are collinear.