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?

Answer 1

To find the coordinates of point C on the line segment AB, we can use the section formula.

Substituting the given values, we can calculate the coordinates of C as (15, 5).

Step-by-step explanation:

In this question, the section formula states that if a line segment AB is divided by a point C in the ratio m:n, then the coordinates of C can be found using the following formula:

Cx = (m*Bx + n*Ax) / (m + n)

Cy = (m*By + n*Ay) / (m + n)

Substituting the given values:

Cx = (3*19 + 5*3) / (3+5)

= 15

Cy = (3*9 + 5*1) / (3+5)

= 5

Therefore, the coordinates of point C are (15, 5).