Question

Hello can you assist With #4 I have done the first part I need the length of PQ

Answer 1

Step 1

The mid-point of NM is P

Using the mid-point theorem:

`(x,y)\text{ = }((x_1+x_2)/(2)\text{ , }(y_1+y_2)/(2))`

We have the coordinates of N and P to be:

N(2,2) , M(3,2)

The coordinates of P is :

`\begin{gathered} (x,y)\text{ = (}\frac{2\text{ + 3}}{2}\text{ ,}\frac{2\text{ + 2}}{2}) \\ =\text{ (}(5)/(2)\text{ , }(4)/(2)) \\ =\text{ (2.5, 2)} \end{gathered}`

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:

`\begin{gathered} (x,\text{ y) = (}\frac{1\text{ + 4}}{2}\text{ , }(1+1)/(2)) \\ =\text{ (2.5, 1)} \end{gathered}`

Step 3

The length of PQ can be found using the formula:

`d\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

The coordinates of P and Q are (2.5, 2) and (2.5, 1)

Applying the formula, the length of PQ is:

`\begin{gathered} PQ\text{ = }\sqrt[]{(2.5-2.5)^2+(1-2)^2} \\ =\text{ }\sqrt[]{1} \\ =\text{ 1} \end{gathered}`

Answer:

Length of PQ = 1