Question

If the points (-2,1),(A,B),(4,-1) are collier and A-B=1. Find the value of A& B

Answer 1

Answer:

(A, B) = (1, 0)

Step-by-step explanation:

Since the points are collinear, the gradient of the segment from (-2, 1) to (A, B) is equal to the gradient of the segment from (-2, 1) to (4, -1).

The gradient is (difference between y coords) / (difference between x coords) so we need

( B - 1 ) / ( A - (-2) ) = ( -1 - 1 ) / ( 4 - (-2) )

=> ( B - 1 ) / ( A + 2 ) = -2 / 6 = -1 / 3

=> 3B - 3 = -A - 2

But we are told that A - B = 1, so A = B + 1.  Putting this into our equation above, we get

3B - 3 = - ( B + 1 ) - 2 = -B - 1 - 2 = -B - 3

=> 4B = 3 - 3 = 0

=> B = 0.

Finally, A = B + 1 = 0 + 1 = 1.