Question

A (5,9) and B(8, – 4) are two given points and the point Y divides the line-segment AB externally in the ratio 6:3. Find the coordinates of B​

Answer 1

To find the coordinates of point B when a line segment is divided externally in a given ratio, we can determine the coordinates of the dividing point Y using the division ratio formula. From there, we can subtract the coordinates of Y from the coordinates of A to find the coordinates of B.

Step-by-step explanation:

To find the coordinates of point B, we first need to determine the coordinates of point Y. The external division ratio is given as 6:3, which means that for every 9 units along AB, 6 units are towards point A and 3 units towards point B. To determine the coordinates of Y, we can use the formula:

Yx = (6*Ax + 3*Bx)/9 and Yy = (6*Ay + 3*By)/9

Substituting the given values, we get:

Yx = (6*5 + 3*8)/9 = 47/9 ≈ 5.222

Yy = (6*9 + 3*(-4))/9 = 54/9 ≈ 6

Therefore, the coordinates of Y are approximately (5.222, 6).

Now, to find the coordinates of B, we subtract the coordinates of Y from the coordinates of A:

Bx = Ax - Yx = 5 - 5.222 ≈ -0.222

By = Ay - Yy = 9 - 6 = 3

Therefore, the coordinates of B are approximately (-0.222, 3).