Respuesta :
You can always compute the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] using the pythagorean theorem:
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
In your case, we have
[tex]d = \sqrt{(0-a)^2+(a-0)^2} = \sqrt{2a^2}=a\sqrt{2}[/tex]
Answer:
[tex]\sqrt{2}a[/tex]
Step-by-step explanation:
We are asked to find the distance between point (0,a) and point (a,0) on a coordinate grid.
We will use distance formula to solve our given problem.
The distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex], where D represents distance between two points.
Let point [tex](0,a)=(x_1,y_1)[/tex] and point [tex](a,0)=(x_2,y_2)[/tex].
Substitute the values in distance formula:
[tex]D=\sqrt{(0-a)^2+(a-0)^2}[/tex]
[tex]D=\sqrt{(-a)^2+(a)^2}[/tex]
[tex]D=\sqrt{a^2+a^2}[/tex]
[tex]D=\sqrt{2a^2}[/tex]
Factor out perfect square:
[tex]D=\sqrt{2}a[/tex]
Therefore, the distance between two points would be [tex]\sqrt{2}a[/tex].
