Respuesta :

qabtt

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:

[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

  • [tex](x_1, y_1)[/tex] is one point
  • [tex](x_2, y_2)[/tex] 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 [tex]D_1[/tex].

[tex]D_1 = \sqrt{(3 - 0)^2 + (1 - 0)^2}[/tex]

[tex]D_1 = \sqrt{3^2 + 1^2}[/tex]

[tex]D_1 = \sqrt{10}[/tex]


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

[tex]D_2 = \sqrt{(1 - 0)^2 + (3 - 0)^2}[/tex]

[tex]D_2 = \sqrt{1^2 + 3^2}[/tex]

[tex]D_2 = \sqrt{10}[/tex]


We can see that [tex]D_1 = D_2[/tex], or that the distances are the same. ✔︎

Both the points are at equal distances from the origin.

Distance between two points on coordinate

Distance between two points on coordinate [tex]=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where,

[tex](x_1, y_1)[/tex] are the coordinates of point 1, and

[tex](x_2, y_2)[/tex] are the coordinates of point 2.

Given to us

  • Point 1, (3, 1)
  • Point 2, (1, 3)

To find

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

Origin

Origin = (0, 0)

Distance of Point 1 from Origin

Distance of (3, 1)  from Origin [tex]=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                                                [tex]=\sqrt{(3-0)^2+(1-0)^2}\\ =\sqrt{(3)^2+(1)^2}\\ =\sqrt{9+1}\\ =\sqrt{10}[/tex]

Distance of Point 2 from Origin

Distance of (1, 3)  from Origin [tex]=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                                                [tex]=\sqrt{(0-3)^2+(0-1)^2}\\ =\sqrt{(-3)^2+(-1)^2}\\ =\sqrt{9+1}\\ =\sqrt{10}[/tex]

As we can see the distance of both points from the origin is [tex]\sqrt{10}[/tex].

Hence, both the points are at equal distances from the origin.

Learn more about Distance between two points:

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