Question

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?

Answer 1

Distance formula:

`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=√(16+9)\\ d=√(25)\\ d=5`

5 units-4.5 units=0.5 units

LM is 0.5 units longer than LM.

Answer 2

Segment LM is 0.5 units longer than segment JK.

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.

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Substitute given values:

`D=√((3-(-1))^2+(1-4)^2)`

`D=√((3+1)^2+(-3)^2)`

`D=√((4)^2+(-3)^2)`

`D=√(16+9)`

`D=√(25)`

`D=5`

Therefore, the distance of segment LM is 5 units.

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

`\text{Difference between LM and JK}=5-4.5`

`\text{Difference between LM and JK}=0.5`

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