Question

Like segment PQ has points at P(7, 2) and Q(1, -1). a. What is the exact lengthb. What is the approximate length?Easy explanation

Answer 1

The distance between two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

From the problem, we identify:

$\begin{gathered} (x_1,y_1)=(7,2) \\ \\ (x_2,y_2)=(1,-1) \end{gathered}$

a.

Using the formula, we calculate the exact length of the segment PQ (which is equal to the distance between the points P and Q):

$\begin{gathered} d=\sqrt{(1-7)^2+(-1-2)^2}=\sqrt{(-6)^2+(-3)^2}=\sqrt{36+9}=\sqrt{45} \\ \\ \therefore d=3\sqrt{5} \end{gathered}$

b.

From the previous answer, the approximate length is:

$\therefore d\approx6.7082$