Question

the point b lies on the segment (overline{ac}). find the coordinates of b so that the ratio of ab to bc is 3 to 4. a (-4,6) b (?,?) c (17,-22) coordinates of b : ( , )

Explanation:

Step1: Recall section - formula

If a point $B(x,y)$ divides the line - segment joining $A(x_1,y_1)$ and $C(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-4,y_1 = 6,x_2=17,y_2=-22,m = 3,n = 4$.

Step2: Calculate the x - coordinate of B

$x=\frac{3\times17+4\times(-4)}{3 + 4}=\frac{51-16}{7}=\frac{35}{7}=5$.

Step3: Calculate the y - coordinate of B

$y=\frac{3\times(-22)+4\times6}{3 + 4}=\frac{-66 + 24}{7}=\frac{-42}{7}=-6$.

Answer:

$(5,-6)$