the endpoints of a segment are given.Calculate the indicated point for each segment. Determine the point that is (1)/(3) the distance from the endpoint (6,24) of the segment with endpoints (-9,-18) and (6,24) Answer format: (45,3.5) Convert fractions to decimals.

To find the point that is $\frac{1}{3}$ the distance from the endpoint $(6,24)$ of the segment with endpoints $(-9,-18)$ and $(6,24)$, we can use the formula for finding a point that divides a line segment in a given ratio.<br /><br />The formula for finding a point that divides a line segment in the ratio $m:n$ is:<br /><br />$\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)$<br /><br />In this case, we want to find the point that divides the line segment in the ratio $1:2$, since we want to find the point that is $\frac{1}{3}$ the distance from the endpoint $(6,24)$.<br /><br />Let's plug in the values into the formula:<br /><br />$\left(\frac{1 \cdot 6 + 2 \cdot (-9)}{1+2}, \frac{1 \cdot 24 + 2 \cdot (-18)}{1+2}\right)$<br /><br />Simplifying the expression, we get:<br /><br />$\left(\frac{6 - 18}{3}, \frac{24 - 36}{3}\right)$<br /><br />$\left(\frac{-12}{3}, \frac{-12}{3}\right)$<br /><br />$\left(-4, -4\right)$<br /><br />Therefore, the point that is $\frac{1}{3}$ the distance from the endpoint $(6,24)$ of the segment with endpoints $(-9,-18)$ and $(6,24)$ is $\left(-4, -4\right)$.