Question

The point M shares the line segment AB in the ratio 1:3. Express CM in terms of x and y.

Options: 1: CM = x + 3y
Options: 2: CM = x - 3y
Options: 3: CM = (x + y) / 4
Options: 4: CM = (x + 3y) / 4

Answer 1

To find CM in terms of x and y, we can use the concept of similar triangles. Since M divides AB in the ratio 1:3, it means that the length of AM is one fourth of the length of AB. Therefore, CM is equal to (x + y)/4.

Step-by-step explanation:

To find CM in terms of x and y, we can use the concept of similar triangles. Since M divides AB in the ratio 1:3, it means that the length of AM is one fourth of the length of AB. We can express this as:

AM = (1/4)AB

Also, we know that AB = x + y (from the given information). So substituting AB = x + y, we get:

AM = (1/4)(x + y)

Since C is the midpoint of AB, CM = AM. Therefore, CM is equal to

CM = (1/4)(x + y)

Therefore, the correct option is: CM = (x + y)/4.