Question

On a number line, the directed line segment from Q to S has endpoints Q at â€"8 and S at 12. Point R partitions the directed line segment from Q to S in a 4:1 ratio. Which expression correctly uses the formula (StartFraction m Over m n EndFraction) (x 2 minus x 1) x 1 to find the location of point R? (StartFraction 1 Over 1 4 EndFraction) (12 minus (negative 8)) (negative 8) (StartFraction 4 Over 4 1 EndFraction) (12 minus (negative 8)) (negative 8) (StartFraction 4 Over 4 1 EndFraction) (negative 8 minus 12) 12 (StartFraction 4 Over 1 4 EndFraction) (negative 8 minus 12) 12.

Answer 1

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Explanation:

The expression that correctly uses the formula \(\frac{m}{m+n}(x_2 - x_1) + x_1\) to find the location of point R is:

\[ \frac{4}{4+1} \cdot (12 - (-8)) + (-8) \]

Let's simplify this expression:

\[ \frac{4}{5} \cdot (20) - 8 \]

\[ \frac{80}{5} - 8 \]

\[ 16 - 8 \]

\[ 8 \]

So, the correct expression is:

\[ \frac{4}{5} \cdot (20) + (-8) = 8 \]

This corresponds to the location of point R on the number line.