The midpoint of a line segment is located at (1, -2). If one of the endpoints is (4, 5), what is the other endpoint? Express your answer as an ordered pair.

Question

The midpoint of a line segment is located at (1, -2). If one of the endpoints is (4, 5), what is the other endpoint? Express your answer as an ordered pair.

Answer 1

The two points on the line are (1,-2) and (4,5). From these two lines, we can deduce the equation of the line.

So, (y+2)/(5+2) = (x-1)/(4-1) which gives the equation as 7x - 3y = 13.

Let the point be (h,k). THis point and the point (4,5) are equidistant from the centre (1,-2).

Let the other point be (h,k). So putting the distance between the two point equation, we have

(4-1)² + (5+2)² = (h-1)² + (k+2)²

Substituting k = (7h-13)/3 in the above equation , and solving for h , we have two values of j

h = 3 and -3.

Solving for k we have two values of k. k = 5, -9.

So the two points are (4,5) and (-2,-9).

Since (4,5) is already one end point, other other point is (-2,-9)