Question

Point Q lies on ST, where point S is located at (-2, -6) and point T is located at (5, 8). If SQ:QT = 5:2,

where is point Q on ST?

my teacher got 0,2 but I don’t know how to find the work to show it. please help!!

Answer 1

`\textit{internal division of a line segment using ratios} \\\\\\ S(-2,-6)\qquad T(5,8)\qquad \qquad \stackrel{\textit{ratio from S to T}}{5:2} \\\\\\ \cfrac{S\underline{Q}}{\underline{Q} T} = \cfrac{5}{2}\implies \cfrac{S}{T} = \cfrac{5}{2}\implies 2S=5T\implies 2(-2,-6)=5(5,8)`

`(\stackrel{x}{-4}~~,~~ \stackrel{y}{-12})=(\stackrel{x}{25}~~,~~ \stackrel{y}{40})\implies Q=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-4 +25}}{5+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-12 +40}}{5+2} \right)} \\\\\\ Q=\left( \cfrac{21}{7}~~,~~\cfrac{28}{7} \right)\implies Q=(3~~,~~4)`