Answered

Segment JK has a length of 4.5 units. If segment LM has end points of L (3,1) and M (-1,4), how much longer than segment JK is segment LM?

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Distance formula:
[tex]d= \sqrt{ (x_{2}-x_{1}) ^{2}+( y_{2} - y_{1} )^{2}}\\ d= \sqrt{ (3-(-1)) ^{2}+(1 - 4 )^{2}}\\ d= \sqrt{ (4) ^{2}+(-3)^{2}}\\ d=\sqrt{16+9}\\ d=\sqrt{25}\\ d=5[/tex]

5 units-4.5 units=0.5 units

LM is 0.5 units longer than LM.

Answer:

Segment LM is 0.5 units longer than segment JK.

Step-by-step explanation:

We have been given that segment JK has a length of 4.5 units. If segment LM has end points of L (3,1) and M (-1,4).

We will find length of segment LM using distance formula.

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute given values:

[tex]D=\sqrt{(3-(-1))^2+(1-4)^2}[/tex]

[tex]D=\sqrt{(3+1)^2+(-3)^2}[/tex]

[tex]D=\sqrt{(4)^2+(-3)^2}[/tex]

[tex]D=\sqrt{16+9}[/tex]

[tex]D=\sqrt{25}[/tex]

[tex]D=5[/tex]

Therefore, the distance of segment LM is 5 units.

Now, we will find the difference between segment LM and JK as:

[tex]\text{Difference between LM and JK}=5-4.5[/tex]

[tex]\text{Difference between LM and JK}=0.5[/tex]

Therefore, segment LM is 0.5 units longer than segment JK.