Question

How do you find the distance between the points (5, 1/4), (3,4)?

Answer 1

`17/4=4.25`

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)=(5,1/4)" and "(x_2,y_2)=(3,4)`

`d=sqrt((3-5)^2+(4-1/4)^2)`

`color(white)(d)=sqrt((-2)^2+(15/4)^2)`

`color(white)(d)=sqrt(4+225/16)`

`color(white)(d)=sqrt(64/16+225/16)`

`color(white)(d)=sqrt(289/16)=17/4=4.25`

Answer 2

`17/4`

Explanation:

`dist( [a, b], (x, y) ) = sqrt{(x - a)^2 + (y - b)^2}`

`d^2 = (5 - 3)^2 + (4 - 1/4)^2`

`d^2 = 4 + 225/16`

`d = sqrt {289/16}`