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K(6, 7) and L(4, 5) are the endpoints of a line segment. What is the midpoint M of that line

segment?
Write the coordinates as decimals or integers.
M =

User Canen
by
7.5k points

2 Answers

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Given:-

  • Two points K(6,7) and L(4,5) .
  • These points are endpoints of a line segment .

To find:-

  • The midpoint of the line segment.

Answer:-

Here we are interested in finding the midpoint of a line segment whose endpoints are given to us . Say if a line segment has endpoints
(x_1,y_1) and
(x_2,y_2) , then the midpoint of the line is given by ,


\implies Midpoint= \bigg((x_1+x_2)/(2),(y_1+y_2)/(2)\bigg) \\

And here , we have;


  • x_1 = 6

  • x_2 = 4

  • y_1 = 7

  • y_2 = 5

So on substituting the respective values, we have;


\implies (x_m , y_m ) =\bigg(( 6+4)/(2),(7+5)/(2)\bigg) \\


\implies (x_m , y_m ) =\bigg( (10)/(2) , (12)/(2)\bigg) \\


\implies\underline{\underline{ (x_m , y_m ) = (5,6)}}\\

Hence the midpoint is (5,6) .

and we are done!

User Mty
by
6.9k points
4 votes

Answer: M = (5, 6)

Formula for midpoint:


\sf (x_m, y_m) = \left((x_1+x_2)/(2), (y_1+y_2)/(2)\right)

Here given:


  • (x_1,y_1) = (6,7), \ (x_2, y_2) = (4,5)

Find midpoint M by substituting values:


\sf M = \left((6+4)/(2), (7+5)/(2)\right)


\sf M = \left((10)/(2), (12)/(2)\right)


\sf M = \left(5, 6\right)