Question

what is the distance between (4, 7) and (2, 2)? choose 1 answer: a $sqrt{10}$ b $sqrt{29}$ c 8 d 9

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 $(x_1,y_1)=(4,7)$ and $(x_2,y_2)=(2,2)$. Then $d=\sqrt{(2 - 4)^2+(2 - 7)^2}$.

Step3: Calculate the differences

$2-4=-2$ and $2 - 7=-5$. So $d=\sqrt{(-2)^2+(-5)^2}$.

Step4: Square the differences

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

Step5: Sum and find square - root

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

Answer:

B. $\sqrt{29}$