Question

What is the distance between P(12, 4) and Q(-8, 2)

Answer 1

$\huge{\boxed{2 \sqrt{101}}}$

The distance formula is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the points.

Substitute in the points. $\sqrt{(2-4)^2+(-8-12)^2}$

Subtract. $\sqrt{(-2)^2+(-20)^2}$

Solve the exponents. $\sqrt{4+400}$

Add. $\sqrt{404}$

Now, we can simplify this square root just a little bit. $404$ has a square factor of $4$. $\sqrt{404}=\sqrt{4}*\sqrt{101}$

The square root of $4$ equals $2$. $\boxed{2 \sqrt{101}}$

Answer 2

Answer: $2\sqrt{101}$

Step-by-step explanation:

The distance between two points can be calculated with the following formula:

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

Given the points  P(12, 4) and Q(-8, 2), we can identify that:

$x_2=-8\\x_1=12\\y_2=2\\y_1=4$

Then, substituing values into the formula, we get that the distance between these two points is:

$d_{(PQ)}=\sqrt{(-8-12)^2+(2-4)^2}\\\\d_{(PQ)}=2\sqrt{101}$