Question

find the distance between each pair of points. remember to simplify the radical. 4) (-3,4), (7,6)

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

Here, $x_1=-3,y_1 = 4,x_2=7,y_2 = 6$. So $d=\sqrt{(7-(-3))^2+(6 - 4)^2}=\sqrt{(7 + 3)^2+(2)^2}$.

Step3: Simplify the expression inside the square - root

$(7 + 3)^2+(2)^2=10^2+4=100 + 4=104$.

Step4: Simplify the radical

$d=\sqrt{104}=\sqrt{4\times26}=2\sqrt{26}$.

Answer:

$2\sqrt{26}$