Question

Find the distance between the two points in simplest radical form.(5,2) and (-1,9)

Answer 1

To answer this question, we need to use the next formula:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

The coordinates for the first point (5, 2) are:

x1 = 5

y1 = 2

The coordinates for the second point (-1, 9) are:

x2 = -1

y2 = 9

Then, we need to apply the previous formula:

`d=\sqrt[]{(-1-5)^2+(9-}2)^2\Rightarrow d=\sqrt[]{(-6)^2+(7)^2}\Rightarrow d=\sqrt[]{36+49}`

Then

`d=\sqrt[]{85}\Rightarrow d=\sqrt[]{5\cdot17}`

Then, we have that the distance between these two points is sqrt(85). We cannot simplify more the expression, since it has two prime numbers and none of them is squared to simplify more the expression.