Point R divides 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?

Question

Point R divides 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?

campbell_st · Answer

well the 1st question is wether the division is internal, between EF, or external, so R is beyond E or F. 

so for internal division I start by writing equivalent ratios 

$$\frac{ER}{RF} = \frac{1}{5}$$

then cross multiply so 

$$5ER = 1RF$$

so you need to multiply the E point by 5 and the F point by 1

then its 

$$x = \frac{5E + F}{ 1 + 5}~~~~y = \frac{5E + F}{1 + 5}$$

so multiply the E point by 5, both x and y

then treat x and y in the same way using the formula... 

Hope it helps

campbell_st · Answer

you always divide by the sum of the parts in the ratio. 

For external division you make 1 part in the ratio negative... it doesn't matter which part.