etermine the point that is 0.75 the distance from the endpoint (-6,-16) of the segment with endpoints (34,2) and (-6,-16) . Answer format: (45,3.5) . Convert fractions to decimals. Type your answer... Skip

To find the point that is 0.75 the distance from the endpoint $(-6,-16)$ of the segment with endpoints $(34,2)$ and $(-6,-16)$, we can use the concept of weighted averages.<br /><br />Let's denote the point we are looking for as $P(x,y)$. Since $P$ is 0.75 the distance from $(-6,-16)$, we can say that $P$ is 0.25 the distance from $(34,2)$.<br /><br />Using the formula for weighted averages, we can write:<br /><br />$x = (-6)(0.25) + (34)(0.75)$<br />$y = (-16)(0.25) + (2)(0.75)$<br /><br />Simplifying these expressions, we get:<br /><br />$x = -1.5 + 25.5 = 24$<br />$y = -4 + 1.5 = -2.5$<br /><br />Therefore, the point that is 0.75 the distance from the endpoint $(-6,-16)$ of the segment with endpoints $(34,2)$ and $(-6,-16)$ is $(24,-2.5)$.