Step 1
The mid-point of NM is P
Using the mid-point theorem:
[tex](x,y)\text{ = }(\frac{x_1+x_2}{2}\text{ , }\frac{y_1+y_2}{2})[/tex]
We have the coordinates of N and P to be:
N(2,2) , M(3,2)
The coordinates of P is :
[tex]\begin{gathered} (x,y)\text{ = (}\frac{2\text{ + 3}}{2}\text{ ,}\frac{2\text{ + 2}}{2}) \\ =\text{ (}\frac{5}{2}\text{ , }\frac{4}{2}) \\ =\text{ (2.5, 2)} \end{gathered}[/tex]
Step 2
The mid-point of KL is Q
We have the coordinates of K and L to be:
K(1, 1), L(4, 1)
The coordinates of Q is:
[tex]\begin{gathered} (x,\text{ y) = (}\frac{1\text{ + 4}}{2}\text{ , }\frac{1+1}{2}) \\ =\text{ (2.5, 1)} \end{gathered}[/tex]
Step 3
The length of PQ can be found using the formula:
[tex]d\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The coordinates of P and Q are (2.5, 2) and (2.5, 1)
Applying the formula, the length of PQ is:
[tex]\begin{gathered} PQ\text{ = }\sqrt[]{(2.5-2.5)^2+(1-2)^2} \\ =\text{ }\sqrt[]{1} \\ =\text{ 1} \end{gathered}[/tex]
Answer:
Length of PQ = 1
