Question

Explain the distance formula. Than use it to calculate the distance between A(1, 1) and B(7, -7).

Answer 1

The answer is 10 units.

Answer 2

The distance between A=(1,1) and B=(7,-7) is 10.

Explanation:

If you have two points
`A=(x_(1),y_(1))` and
`B=(x_(2),y_(2))` the distance between those points is the length of the segment that separates them. And the formula of that distance is:

`d(A,B)=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`

Then the distance between A=(1,1) and B=(7,-7) is:

`x_(1)=1\\y_(1)=1\\x_(2)=7\\y_(2)=-7`

`d(A,B)=√((7-1)^2+((-7)-1)^2)\\d(A,B)=√(6^2+(-8)^2)\\d(A,B)=√(36+64)\\ d(A,B)=√(100) \\d(A,B)=10`

The distance between A=(1,1) and B=(7,-7) is 10.