Question

select the correct answer from each drop - down menu. point c(3.6, - 0.4) divides $overline{ab}$ in the ratio 3:2. if the coordinates of a are (-6, 5), the coordinates of point b are. if point d divides $overline{cb}$ in the ratio 4:5, the coordinates of point d are

Explanation:

Step1: Use section - formula for finding B

The section formula for a point \(C(x,y)\) that divides the line - segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Given \(C(3.6,-0.4)\), \(A(-6,5)\), \(m = 3\), \(n = 2\).
For \(x\) - coordinate of \(B\):

$$3.6=\frac{3x_2+2\times(-6)}{3 + 2}$$

$$3.6\times5=3x_2-12$$

$$18 = 3x_2-12$$

$$3x_2=18 + 12=30$$

$$x_2 = 10$$

For \(y\) - coordinate of \(B\):

$$-0.4=\frac{3y_2+2\times5}{3 + 2}$$

$$-0.4\times5=3y_2 + 10$$

$$-2=3y_2+10$$

$$3y_2=-2 - 10=-12$$

$$y_2=-4$$

So, the coordinates of \(B\) are \((10,-4)\).

Step2: Use section - formula for finding D

Now, point \(D\) divides \(\overline{CB}\) in the ratio \(4:5\), where \(C(3.6,-0.4)\) and \(B(10,-4)\).
For \(x\) - coordinate of \(D\):

$$x_D=\frac{4\times10+5\times3.6}{4 + 5}=\frac{40+18}{9}=\frac{58}{9}$$

For \(y\) - coordinate of \(D\):

$$y_D=\frac{4\times(-4)+5\times(-0.4)}{4 + 5}=\frac{-16 - 2}{9}=\frac{-18}{9}=-2$$

So, the coordinates of \(D\) are \((\frac{58}{9},-2)\)

Answer:

The coordinates of point \(B\) are \((10,-4)\); The coordinates of point \(D\) are \((\frac{58}{9},-2)\)