Question

1. find the coordinate of point y on ac that is 1/4 of the distance from a to c. 15. find the coordinate of point x on af that is 1/3 of the distance from a to f. refer to the number - line.

Explanation:

Step1: Identify coordinates of endpoints

The coordinate of point A is - 5 and the coordinate of point C is - 1.

Step2: Calculate distance between A and C

The distance $d_{AC}=\vert-1-(-5)\vert=\vert-1 + 5\vert=4$.

Step3: Find the position of Y

The point Y is $\frac{1}{4}$ of the distance from A to C. The coordinate of Y is $-5+\frac{1}{4}\times4=-5 + 1=-4$.

Step4: For problem 15, identify endpoints

The coordinate of point A is - 5 and the coordinate of point F is 4.

Step5: Calculate distance between A and F

The distance $d_{AF}=\vert4-(-5)\vert=\vert4 + 5\vert=9$.

Step6: Find the position of X

The point X is $\frac{1}{3}$ of the distance from A to F. The coordinate of X is $-5+\frac{1}{3}\times9=-5 + 3=-2$.

Answer:

1. The coordinate of point X is - 2.
2. The coordinate of point Y is - 4.