Question

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 =

Answer 1

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!

Answer 2

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)`