segmentsFind the other endpoint of a segment, with the endpoint (-1,9) and the midpoint (-9,-10).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The mid point of two point (x1, y1) and (x2, y2) is given by ((x1 + x2)/2 , (y1 + y2)/2)

Here we have the mid point as (-9, -10). Let the point to be determined be (x,y)

This gives us: (x - 1)/2 = -9 and (y + 9)/2 = -10

=> x = -18 + 1 = -17 and y = -20 - 9 = -29

The other point is (-17, -29)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll write the formula of the midpoint, whose endpoints are (x1,y1) and (x2,y2):

xM = (x1 + x2)/2

yM = (y1 + y2)/2

We'll put x1 = -1 and y1 = 9, xM = -9 , yM = -10.

-9 = (-1+x2)/2

We'll multiply by 2:

-18 = x2 - 1

x2 = -17

-10 = (9 + y2)/2

We'll multiply by 2:

-20 = y2 + 9

y2 = -29

The coordinates of the other endpoint are: (-17 , -29).

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