Find the distance between P(1,2) and Q(6,6)

To find the distance between the points P(1, 2) and Q(6, 6), we can use the distance formula:

[

d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}

]

Here, ( (x_1, y_1) ) are the coordinates of point P, and ( (x_2, y_2) ) are the coordinates of point Q.

Plugging in the values:

– ( x_1 = 1 ), ( y_1 = 2 )

– ( x_2 = 6 ), ( y_2 = 6 )

Now, substitute into the formula:

[

d = sqrt{(6 – 1)^2 + (6 – 2)^2}

]

Calculating the differences:

[

d = sqrt{(5)^2 + (4)^2}

]

Calculating the squares:

[

d = sqrt{25 + 16}

]

Adding those together:

[

d = sqrt{41}

]

So, the distance between P and Q is (sqrt{41}).