Question

The line segment joining A(1,-1), B(3,1), is extended to C. If 2BC=3AB. Find the coordinates of C

Answer 1

Answer:

(21/5, 11/5)

Step-by-step explanation:

Hi,

Let the coordinates of the point C be (h, k)

Now, given A(1, -1) and B(3,1)

Also, given that 2BC = 3AB

But, AC = AB + BC, so

2BC = 3(AC - BC)

5BC = 3AC

AC/BC = 5/3

Thus, B is point on AC which divided the segment in the ration 5 : 3

internally.

Using internal sectional formula, coordinated of B will be

(5*h + 3/8, 5*k - 3/8) = (3, 1)

5h + 3/8 = 3 and 5k - 3/8 = 1

5h + 3 = 24 and 5k - 3 = 8

5h = 21 and 5k = 11

h = 21/5 and k = 11/5

Hence, the coordinates of C are (21/5, 11/5)

Hope, it helps !