Question

One endpoint of a line segment is at (6,5). The midpoint of the line segment is at (1,2). Determine the coordinate of the other endpoint.

Answer 1

Midpoint formula =

$m1,m2=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

Where;

(m1,m2 ) = midpoint = (1,2)

(x1,y1) = (6,5)

(x2,y2) ) = ?

For the x coordinate of the missing endpoint:

m1 = (x1+x2) /2

1 = (6 + x2 ) /2

Solve for x2:

1 (2) = 6 + x2

2 = 6 +x2

2-6 = x2

-4 = x2

x2 = -4

Y-coordinate:

m2 = (y1+y2) /2

2 = (5 + y2) /2

Solve for y2

2(2) = 5+ y2

4 = 5 +y2

4-5= y2

-1 = y2

y2= -1

Coordinate: (-4,-1)