Question

if jk has endpoints j(-2,3) and k(6,5), and ln has endpoints l(0,7) and n(4,1), then jk and ln have the same midpoint.

Answer 1

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:

$\frac{x_{1}+ x_{2}}{2}, \frac{y_{1}+ y_{2}}{2}$

Where $x_{1},y_{1}$ are the coordinates of the initial point and $x_{2},y_{2}$ the coordinates of the endpoint

Step 1: Find the  JK's midpoint

For this segment:

J(-2,3); then $x_{1}=-2$ and $y_{1}=3$

K(6,5); then $x_{2}=6$ and  $y_{2}=5$

The coordinates of the midpoint are:

$\frac{x_{1}+ x_{2}}{2}, \frac{y_{1}+ y_{2}}{2}=\frac{-2+6}{2}, \frac{3+5}{2}=2,4$

Step 2: Find the LN's midpoint

For this segment:

L(0,7); then $x_{1}=0$ and $y_{1}=7$

N(4,1); then  $x_{2}=4$ and $y_{2}=1$

The coordinates of the midpoint are:

$\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}=\frac{0+4}{2}, \frac{7+1}{2}=2,4$

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

Answer 2

Ok well, not technically yes, but jk's midpoint is (1,5) and ln is (5,3). So they're not the same. In this case in my opinion, it's no.