Question

Points C and D are on a number line (not shown).

The coordinate of point C is -16 and the coordi-
nate of point D is 14. Point E is a point on line
segment CD. If the distance from point E to point
C is 1/4 the distance from point E to point D, what is
the coordinate of point E?

Answer 1

Answer: -10

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Step-by-step explanation:

I recommend drawing out the number line. Plot -16 and 14 on it.

Either count out the spaces, or subtract and apply absolute value, to find the distance from -16 to 14 is exactly 30 spaces.

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Or you can think of it like this:

From -16 to 0 is 16 spaces

From 0 to 14 is another 14 spaces

That's 16+14 = 30 spaces total.

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In short, segment CD is 30 units long.

Point E is somewhere on segment CD.

x = distance from E to C

y = distance from E to D

x+y = EC+ED = CD = 30

x+y = 30

y = 30-x

We're told the distance from E to C is 1/4 the distance from E to D, so,

x = (1/4)*y

x = (1/4)*(30-x)

x = 0.25*(30-x)

x = 7.5 - 0.25x

x+0.25x = 7.5

1.25x = 7.5

x = (7.5)/(1.25)

x = 6

The distance from E to C is 6 units.

This means we'll add 6 units to the location of point C to find out where to place E

E = C+6 = -16+6 = -10 is the final answer