Question

Point R divides `bar(EF)` in the ratio 1 : 5. If the coordinates of E and F are (4, 8) and (11, 4), respectively, what are the coordinates of R to two decimal places?

Answer 1

5 1/6, 7 1/3

Explanation:

Answer 2

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:
`m=(4-8)/(11-4)=(-4)/(7)`. The coordinates for R are found in the following formula:
`R(x,y)=(x_(1)+k(run),y_(1)+k(rise))`. For us that will look like this:
`R(x,y)=(4+(1)/(6)(7),8+(1)/(6)(-4))`. Simplifying gives us coordinates of R as (5 1/6, 7 1/3)