Question

distance, midpoint, and slope formula practice
find the distance between the pair of points. write in radical form.
(4,3), (-1,6)
d = \sqrt{\square} units

Explanation:

Step1: Identify the 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: Assign the values of the points

Let $(x_1,y_1)=(4,3)$ and $(x_2,y_2)=(-1,6)$. Then $x_1 = 4$, $y_1=3$, $x_2=-1$, $y_2 = 6$.

Step3: Substitute values into the formula

$D=\sqrt{(-1 - 4)^2+(6 - 3)^2}=\sqrt{(-5)^2+3^2}$.

Step4: Calculate the squares

$(-5)^2=25$ and $3^2 = 9$, so $D=\sqrt{25 + 9}$.

Step5: Add the values inside the square - root

$25+9=34$, so $D=\sqrt{34}$.

Answer:

$\sqrt{34}$