Question

What is the distance between `(-1,7)` and `(44,3)`?

Answer 1

See a solution process below:

Explanation:

The formula for calculating the distance between two points is:

`d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)`

Substituting the values from the points in the problem gives:

`d = sqrt((color(red)(44) - color(blue)(-1))^2 + (color(red)(3) - color(blue)(7))^2)`

`d = sqrt((color(red)(44) + color(blue)(1))^2 + (color(red)(3) - color(blue)(7))^2)`

`d = sqrt(45^2 + (-4)^2)`

`d = sqrt(2025 + 16)`

`d = sqrt(2041)`

Or

`d ~= 45.177`

Answer 2

`~~45.18" to 2 dec. places"`

Explanation:

`"calculate the distance using 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)=(-1,7)" and "(x_2,y_2)=(44,3)`

`rArrd=sqrt((44+1)^2+(3-7)^2)`

`color(white)(rArrd)=sqrt(2041)~~45.18`