Respuesta :

maldoengineer

Answer:

Yes, JK and LN have the same midpoint

Step-by-step explanation:

In order to demonstrate that JK and LN have the same midpoint, we have to find their midpoints

The coordinates of the midpoint of a segment are:

[tex]\frac{x_{1}+ x_{2}}{2}, \frac{y_{1}+ y_{2}}{2}[/tex]

Where [tex]x_{1},y_{1}[/tex] are the coordinates of the initial point and [tex]x_{2},y_{2}[/tex] the coordinates of the endpoint

Step 1: Find the  JK's midpoint

For this segment:

J(-2,3); then [tex]x_{1}=-2[/tex] and [tex]y_{1}=3[/tex]

K(6,5); then [tex]x_{2}=6[/tex] and  [tex]y_{2}=5[/tex]

The coordinates of the midpoint are:

[tex]\frac{x_{1}+ x_{2}}{2}, \frac{y_{1}+ y_{2}}{2}=\frac{-2+6}{2}, \frac{3+5}{2}=2,4[/tex]

Step 2: Find the LN's midpoint

For this segment:

L(0,7); then [tex]x_{1}=0[/tex] and [tex]y_{1}=7[/tex]

N(4,1); then  [tex]x_{2}=4[/tex] and [tex]y_{2}=1[/tex]

The coordinates of the midpoint are:

[tex]\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}=\frac{0+4}{2}, \frac{7+1}{2}=2,4[/tex]

Therefore JK's Midpoint and LN's Midpoint are the same

onyebuchinnaji

The mid-point of the given lines is (2,4)

The given end points:

[tex]J = (-2, 3) \ \ and \ \ K = (6,5)\\\\I = (0,7) \ \ \ and \ \ N = (4,1)[/tex]

To find:

The midpoint of the lines

The midpoint of a given line is calculated as:

[tex]mid-point = \frac{x_1 + x_2}{2} , \ \frac{y_1 + y_2}{2}[/tex]

The mid-point of JK is calculated as:

[tex]mid-point \ JK = (\frac{-2 + 6}{2}, \ \frac{3+ 5}{2} ) = (\frac{4}{2} , \frac{8}{2} ) = (2,4)[/tex]

The mid-point of IN is calculated as:

[tex]mid-point \ IN = (\frac{0 + 4}{2}, \ \frac{7+ 1}{2} ) = (\frac{4}{2} , \frac{8}{2} ) = (2,4)[/tex]

Thus, the mid-point of the given lines is (2,4)

Learn more here:https://brainly.com/question/22370589