To find a point that is [tex]\(\frac{1}{4}\)[/tex] of the way from the point [tex]\(-2\)[/tex] to the point [tex]\(5\)[/tex], let's proceed step-by-step.
1. Calculate the distance between the points:
To find the distance between two points on a number line, subtract the smaller point from the larger point. Here, the larger point is [tex]\(5\)[/tex] and the smaller point is [tex]\(-2\)[/tex]. So, the distance is:
[tex]\[
5 - (-2) = 5 + 2 = 7
\][/tex]
2. Determine [tex]\(\frac{1}{4}\)[/tex] of the distance:
Now we need to find what [tex]\(\frac{1}{4}\)[/tex] of this distance is. Since the total distance is [tex]\(7\)[/tex], we calculate:
[tex]\[
\frac{1}{4} \times 7 = \frac{7}{4} = 1.75
\][/tex]
3. Find the point on the line:
Since we are looking for a point that is [tex]\(\frac{1}{4}\)[/tex] of the way from [tex]\(-2\)[/tex] towards [tex]\(5\)[/tex], we start at [tex]\(-2\)[/tex] and move forward [tex]\(1.75\)[/tex] units along the number line. To do this, add [tex]\(1.75\)[/tex] to [tex]\(-2\)[/tex]:
[tex]\[
-2 + 1.75 = -0.25
\][/tex]
Therefore, the point on the number line that is [tex]\(\frac{1}{4}\)[/tex] of the way from [tex]\(-2\)[/tex] to [tex]\(5\)[/tex] is [tex]\(-0.25\)[/tex].
So, the correct answer is:
[tex]\[
-0.25
\][/tex]
