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

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.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute given values:

$D=\sqrt{(3-(-1))^2+(1-4)^2}$

$D=\sqrt{(3+1)^2+(-3)^2}$

$D=\sqrt{(4)^2+(-3)^2}$

$D=\sqrt{16+9}$

$D=\sqrt{25}$

$D=5$

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.

Answer 2

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

5 units-4.5 units=0.5 units

LM is 0.5 units longer than LM.