Question

given the points A{5,-3}, B{-4,9}, C{4,-15} are a straight line, find the ratio in which B divides AC and C divides AB​

Answer 1

To find the ratio in which B divides AC and C divides AB, use the distance formula to calculate the distances between the points. Then, calculate the ratios using the distances obtained.

Step-by-step explanation:

To find the ratio in which B divides AC and C divides AB, we need to calculate the distances between the points.

Using the distance formula, the distance between points A and C is:

d(AC) = sqrt((4-5)^2 + (-15-(-3))^2) = sqrt(1^2 + (-12)^2) = sqrt(1 + 144) = sqrt(145)

The distance between points A and B is:

d(AB) = sqrt((-4-5)^2 + (9-(-3))^2) = sqrt((-9)^2 + 12^2) = sqrt(81 + 144) = sqrt(225) = 15

Now, we can calculate the ratios:

Ratio in which B divides AC = d(AC) / d(AB) = sqrt(145) / 15

Ratio in which C divides AB = d(AB) / d(AC) = 15 / sqrt(145)