Question

Find the coordinates of the other endpoint when you are given the midpoint (point M) and one of the endpoints (point P).

P = (10, 6) and M = (-4, 8)

Answer 1

The coordinates of the other end point is (-18,10).

Explanation:

Let the coordinates of other point is Q(x,y)

⇒ M(-4,8) is the mid point of P(10,6) and Q(x,y).

MID-POINT FORMULA states that for a mid point (a,b):

`(a,b) =( (x_1+x_2)/(2) , (y_1+y_2)/(2) )`

Applying the same mid point formula here, we get:

`(-4,8) =( (10 + x)/(2) , (6+y)/(2) )`

or,
`((10+x)/(2))   = -4 \implies  x = -8 -10 = -18`

and
`((6+y)/(2)  ) = 8 \implies  x = 16 -6 =  10`

or, (x,y) = (-18, 10)

or, the coordinates of Q is (-18,10)

Hence, the coordinates of the other end point = (-18,10)