The endpoints of EF are (4, 8) and (11, 4). We need to find the coordinates of point R that divides EF into a 1:5 ratio. A 1:5 ratio means we need to divide EF into 1+5 equal length partitions, or 6. Point R divides EF into a 1:5 ratio, so R is 1/6 of the from E to F. That ratio is k, found by writing the numerator of the ratio (1) over the sum of the numerator and denominator (6). Our k is 1/6. Now we will find the rise and the run (slope) of the segment between E and F using the slope formula: [tex] m=\frac{4-8}{11-4}=\frac{-4}{7} [/tex]. The coordinates for R are found in the following formula: [tex] R(x,y)=(x_{1}+k(run),y_{1}+k(rise)) [/tex]. For us that will look like this: [tex] R(x,y)=(4+\frac{1}{6}(7),8+\frac{1}{6}(-4)) [/tex]. Simplifying gives us coordinates of R as (5 1/6, 7 1/3)
