Question

Find the midpoint of the line segment whose endpoints are (3, 10) and (7, 8).

1. (2,1)
2. (5,9)
3. (11, 12)

Answer 1

The midpoint of line segment is (5,9).

Explanation:

Given : Line segment whose endpoints are (3, 10) and (7, 8).

To find : Find the midpoint of the line segment .

Solution : We have given that endpoints (3, 10) and (7, 8).

By the midpoint segment formula :

Midpoint :

(
`(x_(1)+x_(2))/(2)` ,
`(y_(1)+y_(2))/(2)`).

Here, the coordinate of
`x_(1)` = 3 ,
`x_(2)` = 7 ,

`y_(1)` = 10 ,
`y_(2)` = 8 ,

Plugging values in formula ,

Midpoint =(
`(3+7)/(2)` ,
`(10+8)/(2)`).

Midpoint =(
`(10)/(2)` ,
`(18)/(2)`).

Midpoint = (5 , 9).

Therefore, the midpoint of line segment is (5,9).

Answer 2

Option 2 is correct.

Explanation:

Given the coordinates of lines segment (3, 10) and (7, 8). we have to find the mid-point of given line segment.

Mid-point formula states that if
`(x_1,y_1)` and
`(x_2,y_2)` are the coordinates of end points of line segment then the coordinates of mid-point are

`((x_1+x_2)/(2),(y_1+y_2)/(2))`

∴ Coordinates of mid-point of line segment joining the points (3, 10) and (7, 8) are

`((3+7)/(2),(10+8)/(2))=((10)/(2),(18)/(2))=(5,9)`

Hence, option 2 is correct.