Question

which coordinates for point b divide segment ac into the ratio ab:bc = 2:1? (1,1) (13,0) (8.5,6) (-2,-1)

Explanation:

Step1: Recall 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 \(y=\frac{my_2+ny_1}{m + n}\). Let \(A(x_1,y_1)=(- 5,-3)\) and \(C(x_2,y_2)=(4,3)\) and \(m = 2\), \(n = 1\).

Step2: Calculate the \(x\) - coordinate of \(B\)

\[x=\frac{2\times4+1\times(-5)}{2 + 1}=\frac{8 - 5}{3}=\frac{3}{3}=1\]

Step3: Calculate the \(y\) - coordinate of \(B\)

\[y=\frac{2\times3+1\times(-3)}{2 + 1}=\frac{6-3}{3}=\frac{3}{3}=1\]

Answer:

(1,1)