Find the length of the line segment that joins the points (2, 5) and (9, 8).

Solution:

Given, the two points are (2,5) and (9, 8).

We have to find the length of the line segment.

Using distance formula,

D = \(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

Here, (x₁,y₁) = (2,5) and (x₂,y₂) = (9,8)

Now, length of the line segment = \(\sqrt{(9-2)^{2}+(8-5)^{2}}\)

= \(\sqrt{(7)^{2}+(3)^{2}}\)

= \(\sqrt{49+9}\)

= \(\sqrt{58}\)

Therefore, the length of the line segment is \(\sqrt{58}\)units.

Find the length of the line segment that joins the points (2, 5) and (9, 8).

Summary:

The length of the line segment that joins the points (2,5) and (9,8) is \(\sqrt{58}\)units.