Question

The coordinates of the endpoints of AB are A(3,1) and B(19,9). Point C is on AB and divides it such that AC:BC is 3:5. What are the coordinates of C? Write your answers as integers or decimals. ( , )

Answer 1

The coordinates of point C, which divides the line segment AB in a ratio of 3:5, are approximately (10.875, 4.625).

Step-by-step explanation:

The coordinates of the endpoints of AB are A(3,1) and B(19,9). Point C is on AB and divides it in a ratio of AC:BC, which is 3:5. To find the coordinates of point C, we can use the section formula in the coordinate geometry.

In the section formula, if a line segment AB is divided by a point C in a ratio m:n, then the coordinates of point C (Cx, Cy) are given by:

Cx = (m*Bx + n*Ax) / (m + n)
Cy = (m*By + n*Ay) / (m + n)

Applying this formula to the given coordinates of A(3,1) and B(19,9) and the ratio 3:5, we get:

Cx = (3*19 + 5*3) / (3 + 5) = 87 / 8 = 10.875
Cy = (3*9 + 5*1) / (3 + 5) = 37 / 8 = 4.625

Therefore, the coordinates of point C are approximately (10.875, 4.625).