How do you find the coordinates of the other endpoint of a segment with the given Endpoint: (1,5) midpoint: (1,-6)?

Question

Hazel Anglin · Accepted Answer

undefined To find the coordinates of the other endpoint of a segment, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a segment are the average of the coordinates of its endpoints.

Given the endpoint (1,5) and the midpoint (1,-6), we can use the midpoint formula to find the coordinates of the other endpoint.

Let the coordinates of the other endpoint be (x, y).

Using the midpoint formula:

(x + 1)/2 = 1   and   (y + 5)/2 = -6

Simplifying the equations:

x + 1 = 2   and   y + 5 = -12

Solving for x and y:

x = 1   and   y = -17

Therefore, the coordinates of the other endpoint are (1, -17).

Ethan Adkins · Answer

Start point #" "->P_s->(x_s,y_s)" "->" "(1,-17)#

The distance from mid to end is the same distance from start to mid as mid point is the mean point

Let end point be #P_e#

Let mean point be #P_m#

Let start point be #P_s# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Mid to end #-> P_e-P_m#

Start to mid #-> P_m-P_s #

#color(green)("As distance from mid to each end is the same")#

we have #P_m-P_s= P_e-P_m#.......(1)

Multiply equation (1) by (-1) so that #P_s# is positive

#-P_m+P_s = +P_m - P_e#

Add #P_m# to both sides

#P_s=P_m+P_m-P_e#

#P_s=2P_m-P_e#

#P_s->(x_s,y_s)#

#x_s=2(x_m)-x_e" "->" "2(1)-1=1#

#y_s=2(y_m)-y_e" "->" "2(-6)-5=-17#

#P_s->(x_s,y_s)" "->" "(1,-17)#