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?

A.
(4.66, 7.62)

B.
(6, 6.86)

C.
(5.17, 7.33)

D.
(9.83, 4.67)

Answer 1

Since, Point R divides $\overline{{EF}}$ in the ratio 1 : 5. If the coordinates of E and F are (4, 8) and (11, 4). We have to determine the coordinates of R.

We will use Cross section formula which states:

If a line segment AB with coordinates $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$ is divided by some coordinate C in the ratio $m_{1} : m_{2}$, then the coordinates of C are given by the formula:

$(\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}})$

Here, $x_{1}= 4 , y_{1}= 8 , x_{2}=11 , y_{2}=4 , m_{1}=1, m_{2}=5$

So, coordinates of R = $(\frac{(1 \times 11)+ (5\times 4)}{1+5},\frac{(1 \times 4)+ (5 \times 8)}{1+5})$

= $(\frac{31}{6},\frac{44}{6})$

= (5.17 , 7.33)

So, the coordinates of R are (5.17, 7.33).