Question

to find the distance between those points, you made 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 (3,2) and (9,10).

Explanation:

Step1: Identify coordinates

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

Step2: Substitute into distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ 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 differences

$3-9=-6$ and $2 - 10=-8$. So $d=\sqrt{(-6)^2+(-8)^2}$.

Step4: Square the differences

$(-6)^2 = 36$ and $(-8)^2=64$. Then $d=\sqrt{36 + 64}$.

Step5: Add the results

$36+64 = 100$. So $d=\sqrt{100}$.

Step6: Find the square - root

$\sqrt{100}=10$.

Answer:

10