Question

9. The coordinates of the midpoint of the line AB are (1, 2). The length of the line AB is 10 units.
(a) If the gradient of AB is 0, find the coordinates of A and B.
(b) If the gradient of AB is 3/4, find the coordinates of A and B
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Answer 1

Step-by-step explanation:

Since the slope AB is 0, points A, B, and the midpoint of AB have the same y-coordinate, and AB is a horizontal line segment.  Since AB has length 10, A and B are 5 units left and right of the midpoint.  

 

      A = (-4, 2) and B = (6,2)

 

2. Let M=(1,2).  Line segments AM and BM both have length 5 and, since the slope of AB is 3/4, each of them is the hypotenuse of a right triangle with vertical leg 3 and horizontal leg 4.  

 

     To find A, start at M then move 4 units to the left and 3 units down.      To find B, start at M then move 4 units to the right and 3 units up.

 

   So, A = (-3, -1) and B = (5, 5)