Question

a line segment has (x1,y1) as one endpoint and (xm,ym) as its midpoint. Find the other endpoint (x2,y2)of the line segment in terms of x1,y1,xm, and ym.

Answer 1

A line segment has (x1, y1)as one endpoint and (xm, ym)as its midpoint.

Use the formula? (x2, y2) = (2xm − x1, 2ym − y1) to find the coordinates of the endpoint of a line segment if the coordinates of the other endpoint and midpoint are (1, 8), (−3, −1) and (−7, 16), (3, 6),respectively.

(a) Endpoint: (1, 8), (−3, −1) (x2, y2) = ( , )
(b) Midpoint: (−7, 16), (3, 6) (x2, y2) = ( , )


ANSWER a) (x2,y2) = (2x-x1, 2y-y1) for midpoints m = 1 = {(2(-3)-1), (2(-1)-8)} = (-7,-10)

Answer b) (x2,y2) = (2x-x1, 2y-y1) for midpoints m = 1 = {(2(3)+7), (2(6)+16)} = (13,28)

Answer 2

(x1,y1)

(x2,y2)

(xm,ym)

Midpoint formula is given as below.

((x1 + x2)/2 , (y1 + y2)/2 )

Where

(x1 + x2)/2 = xm ----------- (1)

(y1 + y2)/2 = ym ----------- (2)

Equation (1) implies that;

x1 + x2 = 2xm

x2 = 2xm – x1

Equation (2) implies that;

y1 + y2 = 2ym

y2 = 2ym – y1

Thus the end point is

(x2,y2) = (2xm – x1, 2ym – y1)