Question

the coordinates of the endpoints of ij are i(3, 5) and j(17, 19). point k is on ij and divides it such that ik:jk is 3:4. what are the coordinates of k? write your answers as integers or decimals.

Explanation:

Step1: Recall section - formula

If a point $K(x,y)$ divides the line - segment joining $I(x_1,y_1)$ and $J(x_2,y_2)$ in the ratio $m:n$, then the coordinates of $K$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1 = 3,y_1 = 5,x_2 = 17,y_2 = 19,m = 3,n = 4$.

Step2: Calculate the x - coordinate of K

$x=\frac{3\times17+4\times3}{3 + 4}=\frac{51 + 12}{7}=\frac{63}{7}=9$.

Step3: Calculate the y - coordinate of K

$y=\frac{3\times19+4\times5}{3 + 4}=\frac{57+20}{7}=\frac{77}{7}=11$.

Answer:

$(9,11)$