Question

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

Answer 1

Answer:

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

Step-by-step 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

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

Hence the Distance is  $D=\sqrt{65}$