Question

Find the distance between the two points in simplest radical form. (0,6)(9,-1)​

Answer 1

sqrt(130)

Step-by-step explanation:

distance formula

d^2 = (x1-x2)^2 + (y1-y2)^2 ( this is just Pythagorean theorem)

d^2 = ( 0-9)^2 = ( 6 - -1)^2

d^2 = 81 + 49

d = sqrt(130) = sqrt (5 * 2 * 13) so it is in simplest form

Answer 2

`\sf √(130) \quad is \ the \ distance \ between \ these \ two \ points`

Step-by-step explanation:

Distance of two points is given by the formula:

`\sf Distance = √((x_2 - x_1)^2 + (y_2 - y_1)^2) \quad where\ (x_1, y_1), (x_2, y_2) \ are \ points`

• Here given points are: (0, 6) and (9, -1)

Substituting the values in the equation

`\sf d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

`\sf d = √((9- 0)^2 + (-1 -6)^2)`

`\sf d = √((9)^2 + (-7)^2)`

`\sf d = √(81 + 49)`

`\sf d = √(130)`