Question

point a is at (-2,4) and point c is at (4,7). find the coordinates of point b on $overline{ac}$ such that the ratio of ab to ac is 1 : 3. b = (, )

Explanation:

Step1: Use the 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, $x_1=-2,y_1 = 4,x_2 = 4,y_2 = 7,m = 1,n = 2$ (since if $AB:AC=1:3$, then $AB:BC = 1:2$).

Step2: Calculate the x - coordinate of B

$x=\frac{1\times4+2\times(-2)}{1 + 2}=\frac{4-4}{3}=0$.

Step3: Calculate the y - coordinate of B

$y=\frac{1\times7+2\times4}{1 + 2}=\frac{7 + 8}{3}=5$.

Answer:

$(0,5)$