How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-3.5, -6) and the midpoint M(1.5, 4.5)?

pighead73283r 2022-11-20 Answered
How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-3.5, -6) and the midpoint M(1.5, 4.5)?
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Answers (1)

artirw9f
Answered 2022-11-21 Author has 20 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 information we have gives:
( 1.5 , 4.5 ) = ( - 3.5 + x 2 2 , - 6 + y 2 2 )
To find x 2 we need to solve this equation:
1.5 = - 3.5 + x 2 2
2 × 1.5 = 2 × - 3.5 + x 2 2
3 = 2 × - 3.5 + x 2 2
3 = - 3.5 + x 2
3.5 + 3 = 3.5 - 3.5 + x 2
6.5 = 0 + x 2
6.5 = x 2
x 2 = 6.5
To find y 2 we need to solve this equation:
4.5 = - 6 + y 2 2
2 × 4.5 = 2 × - 6 + y 2 2
9 = 2 × - 6 + y 2 2
9 = - 6 + y 2
9 + 6 = 6 - 6 + y 2
15 = 0 + y 2
15 = y 2
y 2 = 15
The other end point of the segment is: ( 6.5 , 15 )
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