Question

if the y-coordinate of a point P is three times the x-coordinate of point P and OP=10, find the coordinates of point P

Answer 1

Given:

The y-coordinate of a point P is three times the x-coordinate of point P and OP=10

To find:

Find the coordinates of point P

Solution:

From given, we have,

The y-coordinate of a point P is three times the x-coordinate of point P

Let the coordinates of P be (a, 3a)

and OP = 10

here we will use the distance formula for further calculation.

So, we have,

OP = 10

OP² = 10²

(a - 0)² + (3a - 0)² = 100

a² + (3a)² = 100

a² + 9a² = 100

10a² = 100

a² = 10

a = √10

⇒ 3a = 3√10

Therefore, the coordinates of P are (√10 , 3√10)