Question

Find the coordinates of a point A whose distance from the origin (0, 0) is 5 units.

Answer 1

Answer:

Two examples of points that satisfy this condition is (0,5) and (0,-5).

Step-by-step explanation:

Suppose we have two points:

$A = (x_{1}, y_{1})$

$B = (x_{2}, y_{2})$

The distance between these points is:

$D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$

In this question:

B(0,0)

A(x,y)

We have to find x and y.

We have that:

$\sqrt{(x-0)^{2} + (y-0)^{2}} = 5$

$\sqrt{x^{2} + y^{2}} = 5$

$(\sqrt{x^{2} + y^{2}})^{2} = 25$

$x^{2} + y^{2} = 25$

One example of a point:

I will say that x = 0. So

$0^{2} + y^{2} = 25$

$y = \pm \sqrt{25}$

$y = \pm 5$

So two examples of points that satisfy this condition is (0,5) and (0,-5).

Answer 2

The distance formula is a formula that is used to find the distance between two points.

The coordinate of point A is (0, 5)  or   (0, -5).

Distance formula:

Let us consider that, coordinate of point A is (x, y).

The distance between (0,0) and (x, y) is computed as by using distance formula.

                 $Distance=\sqrt{(x-0)^{2}+(y-0)^{2} } \\\\5=\sqrt{(x-0)^{2}+(y-0)^{2} } \\\\x^{2} +y^{2}=25$

All values that satisfies above equation, will be the coordinate of point A.

When x = 0,  

                $y=\sqrt{25} =\pm 5$

The coordinate of point A is (0, 5)  or   (0, -5).

Learn more about the distance formula here:

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