Question

Determine the distance between the two points (-1,-9) and (4,-7)What is the midpoint of the line segment joining the pairs of Points.

Answer 1

Explanation

Finding the distance between the points

The distance between two points (x₁,y₁) and (x₂,y₂) is given by the following formula.

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

Then, we have:

$\begin{gathered} (x_1,y_1)=(-1,-9) \\ (x_2,y_2)=(4,-7) \end{gathered}$$\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=(4-(-1))^2+(-7-(-9))^2 \\ d=(4+1)^2+(-7+9)^2 \\ d=\sqrt{5^2+2^2} \\ d=\sqrt{25+4} \\ d=\sqrt{29} \\ d\approx5.4 \\ \text{ The symbol }\approx\text{ is read 'approximately'.} \end{gathered}$

Finding the midpoint of the line segment joining the points

The midpoint of the line segment P(x₁,y₁) to Q(x₂,y₂) is:

$\text{ Midpoint }=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Then, we have:

$\begin{gathered} \text{ Midpoint }=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{ Midpoint }=(\frac{-1+4}{2},\frac{-9+(-7)}{2}) \\ \text{ Midpoint }=(\frac{3}{2},\frac{-16}{2}) \\ \text{ Midpoint }=(\frac{3}{2},-8) \end{gathered}$Answer

The distance between the given points is √29 units or 5.4 units rounded to the nearest tenth.

The midpoint of the line segment that joins the pairs of points is (3/2,-8).