Question

find the distance between the points (9, 10) and (4, 8). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Substitute the given points

Let $(x_1,y_1)=(9,10)$ and $(x_2,y_2)=(4,8)$. Then $d=\sqrt{(4 - 9)^2+(8 - 10)^2}$.

Step3: Calculate the differences

$4-9=-5$ and $8 - 10=-2$. So $d=\sqrt{(-5)^2+(-2)^2}$.

Step4: Square the differences

$(-5)^2 = 25$ and $(-2)^2=4$. Then $d=\sqrt{25 + 4}$.

Step5: Add the results

$25+4 = 29$. So $d=\sqrt{29}$.

Answer:

$\sqrt{29}$