HELP! help is needed ASAP! help is very much appreciated.

Answer:

Length of side e is 4.12

Length of side f is 4.24

The length of side f is larger than length of side e

Step-by-step explanation:

We are given two line segments e and f. We need to find lengths of both e and f and determine which is larger.

We can use distance formula to calculate lengths of line segments.

The Distance Formula is: [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Finding length of side e:

We are given points (-2,3) and (-1,-1)

here we have [tex]x_1=-2, y_1=3, x_2=-1 , y_2=-1[/tex]

Putting values in distance formula and finding length

[tex]Length \ of \ side \ e= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ e= \sqrt{((-1)-(-2))^2+(-1-(3))^2}\\Length \ of \ side \ e= \sqrt{(-1+2)^2+(-1-3)^2}\\Length \ of \ side \ e= \sqrt{(1)^2+(-4)^2}\\Length \ of \ side \ e= \sqrt{1+16}\\Length \ of \ side \ e= \sqrt{17}\\Length \ of \ side \ e= 4.12[/tex]

So, Length of side e is 4.12

Finding length of side f:

We are given points (2,2) and (-1,-1)

here we have [tex]x_1=2, y_1=2, x_2=-1 , y_2=-1[/tex]

Putting values in distance formula and finding length

[tex]Length \ of \ side \ f= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ f= \sqrt{((-1)-(2))^2+(-1-(2))^2}\\Length \ of \ side \ f= \sqrt{(-1-2)^2+(-1-2)^2}\\Length \ of \ side \ f= \sqrt{(-3)^2+(-3)^2}\\Length \ of \ side \ f= \sqrt{9+9}\\Length \ of \ side \ f= \sqrt{18}\\Length \ of \ side \ f= 4.24[/tex]

So, Length of side f is 4.24

The length of side f is larger than length of side e

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