Question

Find the coordinates of the midpoint of the segment whose endpoints are H(9, 10) and

K(7, 6).
Find HK

Answer 1

mid point formula:
`\text{coordinates of midpoint= }\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right) \\ \text{distance between two points= } √((x_2-x_1)^2+(y_2-y_1)^2))`

Answer 2

Answer: The coordinate of the midpoint is m ( 8 , 8) and the distance HK is 4.5

Explanation:

To find the coordinates of the point of the segment whose endpoints are H(9,10) and K(7,6), we simply use this formula;

m(
`x_(m)` ,
`y_(m)`) = m(
`(x_(1) + x_(2) )/(2)` ,
`(y_(1) + y_(2) )/(2)` )

`x_(1)` = 9
`y_(1)` = 10
`x_(2)` = 7
`y_(2)` = 6

m(
`x_(m)` ,
`y_(m)`) = m (
`(9 + 7)/(2)` ,
`(10 + 6)/(2)` )

= m (
`(16)/(2)` ,
`(16)/(2)` )

=m ( 8 , 8)

The coordinate of the midpoint is m ( 8 , 8)

To find the distance HK,

let D = distance HK

D = √
`(x_(2) - x_(1) )^(2)` +
`(y_(2) - y_(1)) ^(2)`

= √(7 - 9)² + (6 - 10)²

= √(-2)² + (-4)²

= √4 + 16

=√20

= 4.5

The distance HK is 4.5