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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