Question

A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.

Answer 1

It is given that the coordinates of point A are such that its ordinate is twice its abscissa.

So, let the coordinates of point A be (x, 2x).

We have:

`sqrt((x - 4)^2 + (2x - 3)^2) = sqrt(10)`

(x - 4)² + (2x - 3)² = 10

x² + 16 - 8x + 4x² + 9 - 12x = 10

5x² - 20x + 25 = 10

5x² - 20x = 10 - 25

5x² - 20x = - 15

5x² - 20x + 15 = 0

x² - 4x + 3 = 0

x² - x - 3x + 3 = 0

x(x - 1) -3(x - 1) = 0

(x - 1)(x - 3) = 0

x = 1, 3
Thus, the co-ordinates of the point A are (1, 2) and (3, 6).