Question

the distance formula
drag the coordinates into the distance formula in the correct locations.
to find the distance between two points, you make two calculations:
finding the x - distance and the y - distance using the pythagorean theorem.
combine the calculations into the distance formula.
the distance between points (x1,y1) and (x2,y2) is √((x1 - x2)²+(y1 - y2)²).
consider the points (2,3) and (9,10).
√((x1 - x2)²+(y1 - y2)²)
2 3 9 10

Explanation:

Step1: Identify the coordinates

Let $(x_1,y_1)=(3,2)$ and $(x_2,y_2)=(9,10)$.

Step2: Substitute into distance formula

The distance formula is $d = \sqrt{(x_1 - x_2)^2+(y_1 - y_2)^2}$. Substituting the values, we get $d=\sqrt{(3 - 9)^2+(2 - 10)^2}$.

Step3: Calculate the differences

$3-9=-6$ and $2 - 10=-8$.

Step4: Square the differences

$(-6)^2 = 36$ and $(-8)^2=64$.

Step5: Add the squared - values

$36 + 64=100$.

Step6: Take the square - root

$d=\sqrt{100}=10$.

Answer:

10