Question

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (midpoint ​(negative 11​,13​), endpoint ​(negative 12​,9​)

Answer 1

Formulae:

• Let the coordinates of two points are A (x₁, y₁) and B (x₂, y₂). If another point P divides the line AB into the ratio p : q, then the coordinates of P is given by

( (qx₁ + px₂)/(p + q) , (qy₁ + py₂)/(p + q) )

• When p : q = 1 : 1, i.e., P being the mid-point of AB, then the coordinates of P becomes

    ( (x₁ + x₂)/2 , (y₁ + y₂)/2 )

Solution:

    If AB a line segment with end points A and B where the coordinates of A is given (- 12, 9) and the mid-point, say C is given (- 11, 13), we have to find the coordinates, say (x, y) of B.

Using the above formula, we get

    - 11 = (- 12 + x)/2

or, - 12 + x = - 22

or, x = - 22 + 12

or, x = - 10

& 13 = (9 + y)/2

or, 9 + y = 26

or, y = 26 - 9

or, y = 17

Therefore, the coordinates of the other end is (- 10, 17).

Answer 2

Answer:

the coordinates of the other endpoint = ( -10 , 17)

Step-by-step explanation:

Let say other End point is ( x , y)

Mid point = ( - 11 , 13)

One End = (-12 , 9)

Mid point  =  (one End + other end)/2

=> (-11 , 13)  =  ( -12 + x)/2  , (9 + y)/2

=> -11 = ( -12 + x)/2

=> -12 + x = - 22

=> x = -10

&

13 =  (9 + y)/2

=> 26 = 9 + y

=> y = 17

Hence other end is ( -10 , 17)

the coordinates of the other endpoint = ( -10 , 17)