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
