Question

What is the length of the line segment whose endpoints are A(-1,9) and B(7,4) in the simplest radical form?

Answer 1

`\sf √(89)`

Step-by-step explanation:

Let A =
`\sf (x_1,y_1)` = (-1, 9)

Let B =
`\sf (x_2,y_2)` = (7, 4)

Distance formula:

`\sf d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Input values into the distance formula and solve for d:

`\sf \implies d=√((7-(-1))^2+(4-9)^2)`

`\sf \implies d=√(8^2+(-5)^2)`

`\sf \implies d=√(64+25)`

`\sf \implies d=√(89)`

Answer 2

length :
`\sf √(89)`

Step-by-step explanation:

use the distance formula :
`\sf √((x_2-x_1)^2+(y_2-y_1)^2)`

• using the formula:

`\sf \rightarrow \sf \sf √((7--1)^2+(4-9)^2)`

`\sf \rightarrow \sf \sf √((8)^2+(-5)^2)`

`\sf \rightarrow \sf \sf √(64+25)`

`\sf \rightarrow \sf \sf √(89)`