Find 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 midpoint of two points (x1, y1) and (x2, y2) is given by [(x1+x2)/2 , (y1+ y2)/2]

Now we are given the midpoint as (-9,-10) and one of the end points as (-1,9).

Let teh point we need to find be (X , Y)

Therefore (X -1) / 2 = -9

=> X - 1 = -18

=> X = -17

Also, (Y + 9)/2 = -10

=> Y + 9 = -29

=> Y = -29

Therefore the other end point is (-17 , -29)

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the endpoint is A(-1,9) and the midpoint is M(-9,-10).

We need to find the coordinates of the other endpoint of the line segment AB.

Then we will assume that the other endpoint is B(Bx, By).

Then we will use the midpoint formula to find the endpoint.

We know that:

Mx = (Ax + Bx)/2

==> -9 = (-1+ Bx)/2

==> -18 = -1 + Bx

==> Bx = -18 + 1= -17

==> Bx = -17.

My = (Ay+By)/2

==> -10 = (9+By)/2

==> -20 = 9 + By

==> By = -20 -9 = -29

==> By = -29.

Then, the other endpoint B 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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