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)?

2 Answers

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) #

Feb 13, 2017

#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)#