How do you find the coordinates of the other endpoint of a segment with the given endpoint is K(5,1) and the midpoint is M(1,4)?

Cyrus Travis

Cyrus Travis

Answered question

2022-10-27

How do you find the coordinates of the other endpoint of a segment with the given endpoint is K(5, 1) and the midpoint is M(1, 4)?

Answer & Explanation

Adalyn Pitts

Adalyn Pitts

Beginner2022-10-28Added 15 answers

Step 1
The formula to find the mid-point of a line segment give the two end points is:
M = ( x 1 + x 2 2 , y 1 + y 2 2 )
Where M is the midpoint and the given points are:
( x 1 , y 1 ) and ( x 2 , y 2 )
Substituting the values from the points in the problem gives:
( 1 , 4 ) = ( 5 + x 2 2 , 1 + y 2 2 )
We can now solve for x 2 and y 2
x 2
5 + x 2 2 = 1
2 × 5 + x 2 2 = 2 × 1
2 × 5 + x 2 2 = 2
5 + x 2 = 2
5 - 5 + x 2 = 2 - 5
0 + x 2 = - 3
x 2 = - 3
y 2
1 + y 2 2 = 4
2 × 1 + y 2 2 = 2 × 4
2 × 1 + y 2 2 = 8
1 + y 2 = 8
1 - 1 + y 2 = 8 - 1
0 + y 2 = 7
y 2 = 7
The Other End Point Is: ( - 3 , 7 )

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