Pis a point (8,11). q is a point on the y-axis so that pq=10. find the coordinates of q.

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

Step-by-step 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).

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this