Question

2/3 - 10/9and5/3 and 7/9

Answer 1

Explanation:

Point 1 (
`(2)/(3)` ,
`(-10)/(9)`) in the form (x1,y1)

Point 2 (
`(5)/(3)` ,
`(-7)/(9)`) in the form (x2,y2)

use the distance formula

dist = sqrt[ (x2-x1)^2 + (y2-y1)^2 ]

dist = sqrt [
`(5)/(3)` -
`(2)/(3)`)^2 + (
`(-7)/(9)` - (
`(-10)/(9)` ) )^2 ]

dist = sqrt [ (
`(3)/(3)`)^2 + (
`(3)/(9)`)^2 ]

dist = sqrt [ 1 + (
`(1)/(3)`)^2 ]

dist = sqrt [
`(9)/(9)` +
`(1)/(9)` ]

dist =
`\sqrt{(10)/(9) }`

dist =
`√(10)` *
`\sqrt{(1)/(9) }`

dist =
`√(10)` *
`(1)/(3)`

dist =
`(√(10) )/(3)`

Answer 2

Explanation:

always Pythagoras with the coordinate differences as sides and the distance the Hypotenuse.

c² = (2/3 - 5/3)² + (-10/9 - -7/9)² = (-3/3)² + (-10/9 + 7/9)² =

= (-1)² + (-3/9)² = 1 + (-1/3)² = 1 + 1/9 = 10/9

c = sqrt(10)/3