Question

Show that the points (3,1) and (1,3) are the same distance from the origin

Answer 1

Let's use the distance formula to find the distance between the origin and each of the points. We can use this to show that the distances are the same. Remember that the distance formula is:

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

• $(x_1, y_1)$ is one point
• $(x_2, y_2)$ is the other point that you are trying the distance to

First, let's find the distance between the points (3, 1) and the origin, (0, 0). We will call this distance $D_1$.

$D_1 = \sqrt{(3 - 0)^2 + (1 - 0)^2}$

$D_1 = \sqrt{3^2 + 1^2}$

$D_1 = \sqrt{10}$

Next, let's find the distance between (1, 3) and the origin, (0, 0). We will call this $D_2$.

$D_2 = \sqrt{(1 - 0)^2 + (3 - 0)^2}$

$D_2 = \sqrt{1^2 + 3^2}$

$D_2 = \sqrt{10}$

We can see that $D_1 = D_2$, or that the distances are the same. ✔︎