Question

What is the length of segment AB with point A and B located at (-4, 1) and (2, 9)

Answer 1

The length of segment AB is 10

Explanation:

The distance formula is d=
`\sqrt{ (x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)`

With the points (-4,1) and (2,9) you know that
`-4=x_(1), 2=x_(2), 1=y_(1) ,9=y_(2)`

Now you put the numbers into the distance formula

d=
`\sqrt{(2-(-4))^(2)+(9-1)^2`

(2-(-4) turns into (2+4) because two negatives equal a positive.

After adding and subtracting you get d=
`\sqrt{6^2+8^2`

You then square
`6^2` and
`8^2` to get
`\sqrt{36+64`

After adding 34+64 you get
`\sqrt{100`, which is 10

So the length of segment AB is 10

Answer 2

The answer is 10 units

Explanation:

The distance between two points or a line segment can be found by using the formula

`d = \sqrt{ ({x1 - x2})^(2) + ({y1 - y2})^(2) } \\`

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4, 1) and (2, 9)

The length of segment AB is

`|AB| = \sqrt{ ({ - 4 - 2})^(2) + ({1 - 9})^(2) } \\ = \sqrt{( { - 6})^(2) + ({ - 8})^(2) } \\ = √(36 + 64) \\ = √(100) \: \: \: \: \: \: \: \: \\ = 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \:`

We have the final answer as

10 units

Hope this helps you