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The point
B lies on the segment
bar(AC).
Find the coordinates of
B so that
AB is
(5)/(8) of
AC.

The point $B$ lies on the segment $\overline{AC}$ . Find the coordinates of $B$ so that $AB$ is $\frac{5}{8}$ of $AC$ .

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Translations: find the coordinates

Full solution

Q. The point

B

lies on the segment

\overline{AC}

. Find the coordinates of

B

so that

AB

is

\frac{5}{8}

of

AC

.

Identify Coordinates: Identify the coordinates of points $A$ and $C$ , assuming $A$ is at $(0,0)$ and $C$ is at $(8,0)$ for simplicity.
Calculate Distance AC: Calculate the distance AC, which is the difference in x-coordinates of C and A. $AC = 8 - 0 = 8$ .
Determine Ratio of AB to AC: Determine the ratio of $AB$ to $AC$ , which is given as $\frac{5}{8}$ .
Calculate x-coordinate of B: Calculate the x-coordinate of B using the ratio. $x$ -coordinate of $B = 0 + \left(\frac{5}{8}\right)*8 = 5$ .

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million metric tons. The US is the secondlargest emiuer of

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713

million metric tons. India is the thirdlargest emitter, with

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