Question

refer to the number line. find the coordinate of point y on $overline{ac}$ that is $\frac{1}{4}$ of the distance from a to c.

Explanation:

Step1: Identify coordinates of A and C

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

Step2: Calculate the distance between A and C

The distance $d$ between two points $x_1$ and $x_2$ on a number - line is $d=\vert x_2 - x_1\vert$. Here, $x_1=-5$ and $x_2 = - 1$, so $d=\vert-1-(-5)\vert=\vert-1 + 5\vert = 4$.

Step3: Find the distance from A to Y

We want to find the point Y which is $\frac{1}{4}$ of the distance from A to C. The distance from A to Y is $\frac{1}{4}\times4 = 1$.

Step4: Calculate the coordinate of Y

To find the coordinate of Y, we start from the coordinate of A and move 1 unit towards C. Let the coordinate of Y be $x$. Then $x=-5 + 1=-4$.

Answer:

-4