Question

select the correct answer from each drop - down menu. point c(3, 6, - 0.4) divides ab in the ratio 3:2. if the coordinates of a are (- 6, 5), the coordinates of point b are. if point d divides cb in the ratio 4:5, the coordinates of point d are.

Explanation:

Step1: Find coordinates of B using section - formula for C dividing AB.

Let coordinates of \(B\) be \((x,y)\). For a point \(C(x_c,y_c)\) dividing the line - segment joining \(A(x_a,y_a)\) and \(B(x,y)\) in the ratio \(m:n\), the section formula is \(x_c=\frac{mx + nx_a}{m + n}\) and \(y_c=\frac{my+ny_a}{m + n}\). Here \(A(-6,5)\), \(C(3, - 4)\), \(m = 3\), \(n = 2\).
\(3=\frac{3x+2\times(-6)}{3 + 2}\), \(15 = 3x-12\), \(3x=27\), \(x = 9\); \(-4=\frac{3y + 2\times5}{3+2}\), \(-20=3y + 10\), \(3y=-30\), \(y=-10\). So \(B(9,-10)\).

Step2: Find coordinates of D using section - formula for D dividing CB.

Now, for \(D\) dividing \(CB\) where \(C(3,-4)\), \(B(9,-10)\) in the ratio \(4:5\). Let coordinates of \(D\) be \((x_d,y_d)\). Then \(x_d=\frac{4\times9+5\times3}{4 + 5}=\frac{36 + 15}{9}=\frac{51}{9}=\frac{17}{3}\), \(y_d=\frac{4\times(-10)+5\times(-4)}{4 + 5}=\frac{-40-20}{9}=\frac{-60}{9}=-\frac{20}{3}\).

Answer:

\(D(\frac{17}{3},-\frac{20}{3})\)