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What point on the number line is [tex] \frac{1}{4} [/tex] of the way from the point [tex] -2 [/tex] to the point [tex] 5 [/tex]?

A. [tex] -0.25 [/tex]
B. [tex] -0.5 [/tex]
C. 1.75
D. 3.25


Sagot :

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]