Question

Pic below ......................................

Answer 1

Answer:

$d = \sqrt{65}$

Step-by-step explanation:

We need to find the distance between the points (5, 2) and (1, 9). In order to do this, we will use something called the distance formula. The distance formula is written as follows:

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

Now we need to plug in our points which we have given in the form (x, y):

$d = \sqrt{(5-1)^{2}+(2-9)^{2}}$

Next, perform the operation of subtraction inside the parentheses to simplify:

$d = \sqrt{(4)^{2}+(-7)^{2}}$

The exponent is the next step in the order of operations, so square 4 and -7:

$d = \sqrt{16+49}$

Finally, add 16 to 49:

$d = \sqrt{65}$

The square root of 65 cannot be simplified further, but an approximation can be made.

$\sqrt{65}$  ≈ 8.062257748