Final answer:
To calculate the ratio in which the line joining points A(-4,2) and B(3,6) is divided by point P(x,3), we need to find the distance between points A and B and the distance between point A and point P. By solving the equation, we find that x is approximately 2.
Step-by-step explanation:
To calculate the ratio in which the line joining points A(-4,2) and B(3,6) is divided by point P(x,3), we need to find the distance between points A and B and the distance between point A and point P.
Distance between A and B: √[(x2 - x1)^2 + (y2 - y1)^2] = √[(3 - (-4))^2 + (6 - 2)^2] = √[49 + 16] = √65
Distance between A and P: √[(x2 - x1)^2 + (y2 - y1)^2] = √[(x - (-4))^2 + (3 - 2)^2] = √[(x + 4)^2 + 1]
The ratio in which the line AB is divided by point P is given by (Distance between A and P) / (Distance between A and B) = (√[(x + 4)^2 + 1]) / √65. To find the value of x, we need to solve the equation (√[(x + 4)^2 + 1]) / √65 = 1/x.
By solving this equation, we find that x is approximately 2. Therefore, the correct answer is D. x = 2.