Question

The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is , then the coordinates of the point are

• A. (1,2) or (3,6)
• B. (2,1) or (6,3)
• C. (1,2) or (3,5)
• D. (2,1) or (3,6)

Answer 1

The correct option is A

(1,2) or (3,6)

Let the coordinates of the point be P(x,2x). Let Q be the point (4,3).

PQ²=(4-x)²+(3-2x)² = 10

16+x²-8x+9+4x²-12x=10

5x²-20x+15=0

x²-4x+3=0

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

x=1 or x=3

So, 2x = 2 or 6

Hence, the coordinates of the required point are (1,2) or (3,6).