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: Determine coordinates of A and C

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

Step2: Use distance formula on number - line

The distance 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 \(d=\vert-1-(-5)\vert=\vert-1 + 5\vert=\vert4\vert = 4\).

Step3: Find the position of Y

We want to find a point Y on \(\overline{AC}\) that is \(\frac{1}{4}\) of the distance from A to C. Let the coordinate of Y be \(y\). The formula to find \(y\) is \(y=x_1+\frac{1}{4}(x_2 - x_1)\). Substituting \(x_1=-5\) and \(x_2=-1\) into the formula: \(y=-5+\frac{1}{4}(-1-(-5))=-5+\frac{1}{4}(4)=-5 + 1=-4\).

Answer:

The distance from A to C is 4 and the coordinate of point Y is - 4.