Question

Which expression gives you the distance between the points (5,1)and(9,-6)

Answer 1

`D=\sqrt{(x_(2)-x_(1))^(2) +(y_(2)-y_(1))^(2) }`

Explanation:

Here we are supposed to find the distance between the two coordinates in a plane. The coordinates given to us are

(5,1) and (9,-6)

We can find the distance using distance formula. The distance formula is given as

`D=\sqrt{(x_(2)-x_(1))^(2) +(y_(2)-y_(1))^(2) }`

Where

`(x_(2),y_(2)) ; (x_(1),y_(1))`

are the two coordinates

Hence

`x_(2) = 9 ; y_(2)= -6\\x_(1)=5; y_(1)=1`

Substituting these values in the distance formula we get

`D=\sqrt{(9-5)^(2) +(-6-1)^(2)}\\D=\sqrt{(4)^(2) +(-7)^(2)}\\D=√(16+49)\\D=√(65)\\`

Hence the Distance is
`D=√(65)\\`