Question

P and Q are two points lying on the x - axis and the y-axis respectively . Find the coordinates of P and Q if the difference between the abscissa of P and the ordinates of Q is 1 and PQ is 5 units.

Answer 1

P lies on x-axis and Q lies on y-axis

Let abscissa P be x then ordinate of Q is x - 1

∴ P(x , 0) , Q (0 , x - 1)

Given PQ = 5 units

`sqrt (("x" - 0)^2 + (0 - x + 1)^2) = 5`

squaring both sides

x² + x² + 1 - 2x = 25

2x² - 2x - 24 = 0

x² - x - 12 = 0

x² - 4x + 3x - 12 = 0

(x - 4)(x + 3) = 0

x = + 4 or - 3

Coordinates of P are (4,0) or (-3,0)

Coordinates of Q are (0,3) or (0,-4)