Answer:
The possible co-ordinates of the point Q are (0,5) and (0,17).
Explanation:
Given:
P is a point (8,11)
Q is point on y-axis
PQ = 10 units
To find co-ordinates of point Q.
Solution:
Any point on y-axis is given as
as
at y-axis.
Let the point Q be =

We use the distance formula to find length of PQ.
By distance formula:
The distance between two points
and
is given as:

Thus, for the point P(8,11) and Q(0,
) the distance PQ can be given as:



Substituting PQ=10 units.

Squaring both sides.


Subtracting both sides by 64.


Taking square root both sides.


So, we have two equations to solve:
and

Adding
both sides.
and

and

Subtracting both sides by 6 for one equation and adding 6 both sides for the other equation.
and

∴
and
Thus, the possible co-ordinates of the point Q are (0,5) and (0,17).