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P is a point (8,11). Q is a point on the y-axis so that PQ=10. Find the coordinates of Q.

User Nik Graf
by
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1 Answer

7 votes

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
(0,y) as
x=0 at y-axis.

Let the point Q be =
(0,y)

We use the distance formula to find length of PQ.

By distance formula:

The distance between two points
(x_1,y_1) and
(x_2,y_2) is given as:


d=√((x_1-x_2)^2+(y_1-y_2)^2)

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


PQ=√((8-0)^2+(11-y)^2)


PQ=√((8)^2+(11-y)^2)


PQ=√(64+(11-y)^2)

Substituting PQ=10 units.


10=√(64+(11-y)^2)

Squaring both sides.


10^2=(√(64+(11-y)^2))^2


100=64+(11-y)^2

Subtracting both sides by 64.


100-64=64-64+(11-y)^2


36=(11-y)^2

Taking square root both sides.


√(36)=√((11-y)^2)


\pm6=11-y

So, we have two equations to solve:


6=11-y and
-6=11-y

Adding
y both sides.


6+y=11-y+y and
-6+y=11-y+y


6+y=11 and
-6+y=11

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


6-6+y=11-6 and
-6+6+y=11+6


y=5 and
y=17

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

User Kaan Baris
by
8.1k points

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