Question

the coordinates of the endpoints of cd are c(-6, -1) and d(6, 5). point e is on cd and divides it such that ce:de is 1:5. what are the coordinates of e? write your answers as integers or decimals.

Explanation:

Step1: Recall the section - formula

If a point $E(x,y)$ divides the line - segment joining $C(x_1,y_1)$ and $D(x_2,y_2)$ in the ratio $m:n$, then the coordinates of $E$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 1$, $n = 5$, $x_1=-6$, $y_1=-1$, $x_2 = 6$, and $y_2 = 5$.

Step2: Calculate the x - coordinate of E

$x=\frac{1\times6+5\times(-6)}{1 + 5}=\frac{6-30}{6}=\frac{-24}{6}=-4$.

Step3: Calculate the y - coordinate of E

$y=\frac{1\times5+5\times(-1)}{1 + 5}=\frac{5 - 5}{6}=0$.

Answer:

$(-4,0)$