Question

Help please!!!

What is the distance between the two endpoints in the graph below? If necessary, round your answer to two decimal places.

Answer 1

A) 7.07

Explanation:

`The \: distance \: formula = \sqrt{(x_2 - x_1) ^(2) + (y_2 - y_1) ^(2) }`

`P_1(-3, -2) \: \: \: \: \: \: \: \: \: \: \: P_2(2, 3)`

`d = \sqrt{ {(2 - ( - 3))}^(2) + {(3 - ( - 2))}^(2) } \\ d = \sqrt{ {(2 + 3)}^(2) + {(3 + 2)}^(2) } \\ d = \sqrt{ {5}^(2) + {5}^(2) } \\ d = √(25 + 25) \\ d = √(25(1 + 1)) \\ d = √(25(2)) \\ d = √(25) * √(2) \\ d = 5 √(2) \\d = 7.07106781187 \\ d = 7.07`

Answer 2

Answer: A. 7.07 units

Explanation:

The distance between any two points (a,b) and (c,d) is given by :-

`D=√((d-b)^2+(c-a)^2)`

From the given picture , we can see that the line is passing through (2,3) and (-3,-2).

The distance between (2,3) and (-3,-2) is given by :-

`D=√((-2-3)^2+(-3-2)^2)\\\\\Rightarrow\ D=√((-5)^2+(-5)^2)\\\\\Rightarrow\ D=√(25+25)=√(50)\\\\\Rightarrow\ D=7.07106781187\approx7.07`

Hence, the distance between the two endpoints = 7.07 units