Question

find the value of t if the points (t, 2t)(2t,6t)and (3,8) are collinear​

Answer 1

Answer: So this is our answer

Step-by-step explanation:

Answer 2

Given are the coordinates of three collinear points, Find the value of 't'.

Explanation:

• The given three points are said to be collinear if and only if they lie on the same straight line.
• Therefore, for the given three points we know that one point should satisfy the equation of line formed by the other two points.
• Here we have the points $A(t,2t),\ B(2t,6t),\ C(3,8)$.
• Now the equation of a line formed by two coordinate points is given by,            $x-x_1=(\frac{y_2-y_1}{x_2-x_1} )(y-y_1)$      
• Hence the equation of the line joining the points A and B is given by,
•                $->x-t=(\frac{6t-2t}{2t-t} )(y-2t) \\->x-t=4y-8t\\->x-4y+7t=0$    
• Now putting the point C in the equation of line AB we get,
•               $->3-4(8)+7t=0\\->7t=29\\->t=\frac{29}{7}$    
• Hence for the points $(t,2t),\ (2t,6t),\ (3,8)$ to be collinear the value of 't' should be equal to $\frac{29}{7}$.