Question

write the coordinates of points on y axis which are at distance of 5 units from the origin. How many such points are there
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Answer 1

Given,

The points are situated on the y-axis.

The pointa have a distance of 5 units from the origin.

To find,

The coordinates of those points and number of possible points.

Solution,

We know that, any point on the y-axis has an ordinate of zero and the coordinates of the origin is (0,0).

Let, the abscissa of the point = y (when the point is on the positive side of the y axis)

Distance between the origin and the point :

= ✓(0-0)²+(0-y)²

= ✓y²

= y

According to the question,

y = 5

So, the coordinates of the point = (0,5)

Now, the same procedure can be applied when the point is on the negative side of the y axis. Then we will get that the ordinate will be -5.

Coordinate of the second point = (0,-5)

Verification :

Distance between second point and the origin

= ✓(0-0)²+(-5+0)²

= ✓(0+25)

= ✓25

= 5 units

= As mentioned in the question

So, there will be two possible points.

Hence, there will be two possible points and the coordinates are (0,5) and (0,-5).

Answer 2

Given : points on y axis  are at distance of 5 units from the origin.

To Find :  the coordinates of points

How many such points are there

Solution:

points on y axis

x coordinate are are zero

Let say y coordinate is a

Hence point is ( 0 , a)

Using distance formula

Distance from origin is 5

5 = √(0 - 0)² + (a - 0)²

=> 5 = √0 + a²

=> 5  = √a²

=>  5 = | a |

=> a =  ± 5

Hence two such point exist

( 0 , 5)  and ( 0 , - 5)

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