Question

in line segment ab with endpoints a(-3,-4) and b(6,14), the point p divides ab in a ratio of 5:4 from point b. determine the coordinates of point p.

Explanation:

Step1: Recall the section - formula

If a point $P(x,y)$ divides the line - segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $m:n$ from $B$, then the coordinates of $P$ are given by $x=\frac{mx_1+nx_2}{m + n}$ and $y=\frac{my_1+ny_2}{m + n}$. Here, $x_1=-3,y_1=-4,x_2 = 6,y_2 = 14,m = 5,n = 4$.

Step2: Calculate the x - coordinate of point P

$x=\frac{5\times(-3)+4\times6}{5 + 4}=\frac{-15 + 24}{9}=\frac{9}{9}=1$.

Step3: Calculate the y - coordinate of point P

$y=\frac{5\times(-4)+4\times14}{5 + 4}=\frac{-20+56}{9}=\frac{36}{9}=4$.

Answer:

$(1,4)$