Question

refer to the number line. find the coordinate of point h that is $\frac{1}{5}$ of the distance from c to f.

Explanation:

Step1: Find the distance between C and F

The coordinate of C is - 3 and the coordinate of F is 5. The distance $d$ between two points on a number - line is given by $d=\vert x_2 - x_1\vert$. Here, $d=\vert5-(-3)\vert=\vert5 + 3\vert = 8$.

Step2: Calculate the distance from C to H

We want to find the point H that is $\frac{1}{5}$ of the distance from C to F. So the distance from C to H, $d_{CH}=\frac{1}{5}\times d$. Substituting $d = 8$, we get $d_{CH}=\frac{1}{5}\times8=\frac{8}{5}=1.6$.

Step3: Find the coordinate of H

Since we are moving from C towards F (in the positive direction), if the coordinate of C is $x_C=-3$, then the coordinate of H, $x_H=x_C + d_{CH}$. So $x_H=-3 + 1.6=-1.4$.

Answer:

-1.4