Question

What is the distance between (8, -3) and (4, -7)?

Answer 1

`4sqrt2~~5.66" 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)=(8,-3)" and "(x_2,y_2)=(4,-7)`

`d=sqrt((4-8)^2+(-7+3)^2)`

`color(white)(d)=sqrt(16+16)=sqrt32=4sqrt2~~5.66`

Answer 2

`=> d = 4sqrt(2)`

Explanation:

In 2D cartesian coordinates, distance between two points is given as:

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

So for our problem:

`=> d = sqrt((4-8)^2 + (-7-(-3))^2)`

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

`=> d = sqrt(16+16)`

`=> d=sqrt(32)`

Now we can simplify by trying to find the largest square number we can pull out of the square root.

`=> d = sqrt(2xx16)`

`=> d = sqrt(2 xx 4^2)`

`=> d = 4sqrt(2)`