Question

In the coordinate plane, what is the length of the line segment that connects points at (5, 4) and (−3, −1)?

Enter your answer in the box. Round to the nearest hundredth.

Answer 1

• (5,4)
• (-3,-1)

Distance:-

• √(x2-x1)²+(y2-y1)²
• √(-3-5)²+(-1-4)²
• √(-8)²+(-5)²
• √64+25
• √89
• 9.43

Answer 2

9.43 (nearest hundredth)

Explanation:

`\textsf{let}\:(x_1,y_1)=(-3,-1)`

`\textsf{let}\:(x_2,y_2)=(5,4)`

To find the length of the line segment that connects the two given points, we can use the distance formula.

Distance between two points formula

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

(where
`(x_1,y_1)` and
`(x_2,y_2)` are the two points and d is the distance)

Simply substitute the given points into the formula and solve for d:

`\begin{aligned}\implies d &=√((5-(-3))^2+(4-(-1))^2)\\ & =√((8)^2+(5)^2)\\ & = √(64+25)\\ & = √(89)\\ & = 9.43\:\sf(nearest\:hundredth)\end{aligned}`