Question

the point b lies on the segment ac. find the coordinates of b so that ab is 1/4 of ac. a(-1, -2) c(19, 10) b(?,?) coordinates of b: try again

Explanation:

Step1: Use 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 $m:n$, the coordinates of $B$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 1$ and $n=3$ (since $AB=\frac{1}{4}AC$, so the ratio of $AB$ to $BC$ is $1:3$), $x_1=-1,y_1 = - 2,x_2=19,y_2 = 10$.

Step2: Calculate the x - coordinate of B

$x=\frac{1\times19+3\times(-1)}{1 + 3}=\frac{19 - 3}{4}=\frac{16}{4}=4$.

Step3: Calculate the y - coordinate of B

$y=\frac{1\times10+3\times(-2)}{1 + 3}=\frac{10-6}{4}=\frac{4}{4}=1$.

Answer:

$(4,1)$