What is the distance between #(-4, 6)# and # (3,7) #?

2 Answers
Aviv S.
Mar 10, 2018

The distance between the two points is #5sqrt2#.

Explanation:

Using the distance formula,

#color(white)=>d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)#

we can plug in our points,

#color(white)=>P_1=(-4,6)#

#color(white)=>P_2=(3,7)#

and solve for the distance:

#color(white)=>d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)#

#=>d=sqrt((color(red)(-4-3))^2+(color(blue)(6-7))^2)#

#color(white)(=>d)=sqrt((color(red)-color(red)7)^2+(color(blue)-color(blue)1)^2)#

#color(white)(=>d)=sqrt(color(red)49+color(blue)1)#

#color(white)(=>d)=sqrtcolor(purple)50#

#color(white)(=>d)=sqrt(color(purple)(25*2))#

#color(white)(=>d)=sqrt(color(purple)(5^2*2))#

#color(white)(=>d)=sqrtcolor(purple)(5^2)*sqrtcolor(purple)2#

#color(white)(=>d)=color(purple)5*sqrtcolor(purple)2#

#color(white)(=>d)=color(purple)5sqrtcolor(purple)2#

Jim G.
Mar 10, 2018

#5sqrt2~~7.07" to 2 dec. places"#

Explanation:

#"to calculate the distance use the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(-4,6)" and "(x_2,y_2)=(3,7)#

#d=sqrt((3-(-4))^2+(7-6)^2)#

#color(white)(d)=sqrt(49+1)=sqrt50=5sqrt2~~7.07#

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