Question

Use the distance formula to calculate the length of side BC

Answer 1

Given the line segment with end points B and C

Step 1: Write the coordinate of the end points and define the (x,y) values

`\begin{gathered} B(3,2),x_1=3,y_1=2 \\ C(4,-1),x_2=4,y_2=-1 \end{gathered}`

Step 2: Write the formula for the distance between two points

`|BC|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1})^2`

Step 3: Substitute the values of x and y

`\begin{gathered} |BC|=\sqrt[]{(4-3)^2+(-1-2})^2 \\ =\sqrt[]{1^2+(-3^2)} \\ =\sqrt[]{1+9} \\ =\sqrt[]{10}units \end{gathered}`

Hence, the length of the side BC is 3.16 units

OR

`\sqrt[]{10}units`