Question

What is the distance between P and Q and the coordinates of the midpoint of the line segment PQ if P(7,6), Q(7, 2)?

Answer 1

Distance `= 4`
Midpoint `= (7 ,4)`

Explanation:

So first of all to calculate the distance between two points we use the formula below:

distance = `sqrt ((x_2 - x_1)^2+(y_2 -y_1)^2`

So replacing the coordinates in the formula,

distance = `sqrt ((7-7)^2 +(6-2)^2` `= sqrt ((0^2 + 4^2)` `= sqrt 16 = 4`

The midpoint also has an easy formula :

`((x_1 + x_2)/2 , (y_1+y_2)/2)`

So the midpoint is : `((7 + 7)/2 , (6+2)/2) = (14/2, 8/2) = (7 , 4)`

Answer 2

`PQ=4," mid-point "=(7,4)`

Explanation:

To calculate distance use the `color(blue)"distance formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(2/2)|)))`
where `(x_1,y_1),(x_2,y_2)" are 2 coordinate points"`

The 2 points here are (7 ,6) and (7 ,2)

let `(x_1,y_1)=(7,6)" and " (x_2,y_2)=(7,2)`

`rArrd_(PQ)=sqrt((7-7)^2+(2-6)^2)=sqrt(16)=4`

The coordinates of the mid-point are the `color(blue)"average"` of the x and y coordinates of P(7 ,6) and Q(7 ,2)

`rArrx_("midpoint")=1/2(7+7)=7`

`"and " y_("midpoint")=1/2(6+2)=4`

`rArr" coordinates of midpoint "=(7,4)`