The ordinate of a point is twice its abscissa Find the coordinates of the point, if its distance from - Maths - Coordinate Geometry

Question

The ordinate of a point is twice its abscissa Find the
coordinates of the point, if its distance from the point (4,3) is
root 10 units

Fathima Parween · Accepted Answer

let the coordinate of that point be P(x,2x).

let the given point (4,3) be Q(4,3).

Then PQ= $\sqrt{{(4 - x)}^{2} + {(3 - 2 x)}^{2}} = \sqrt{10}$

$\Rightarrow \sqrt{{(4 - x)}^{2} + {(3 - 2 x)}^{2}} = \sqrt{10} S q u a r i n g b o t h s i d e s, \Rightarrow {(4 - x)}^{2} + {(3 - 2 x)}^{2} = 10 \Rightarrow {16 + x}^{2} - 8 x + {9 + 4 x}^{2} - 12 x = 10 \Rightarrow {5 x}^{2} - 20 x + 25 - 10 = 0 \Rightarrow {5 x}^{2} - 20 x + 15 = 0 \Rightarrow x^{2} - 4 x + 3 = 0 \Rightarrow x^{2} - 3 x - x + 3 = 0 \Rightarrow x (x - 3) - 1 (x - 3) = 0 e i t h e r (x - 3) = 0 o r (x - 1) = 0 \Rightarrow x = 3 o r x = 1$

the required two points are (1,2) and (3,6)

The ordinate of a point is twice its abscissa. Find the coordinates of the point, if its distance from the point (4,3) is root 10 units.