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

SAMPLE


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).............................Ans

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

Answer 2

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