Question

Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are .

Answer 1

QUESTION 1

The point  C(3.6, -0.4) divides AB in the ratio 3 : 2.

The coordinates of A are (-6, 5).

Let the coordinates of B be $(x_2,y_2)$

We use the formula:

$x=\frac{mx_2+nx_1}{m+n}$ to determine the x-coordinate of B.

We substitute the known values to obtain:

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

$3.6=\frac{3x_2-12)}{5}$

$3.6\times 5=3x_2-12$

$18=3x_2-12$

$18+12=3x_2$

$30=3x_2$

This implies that:

$x_2=10$

We also use the formula:

$y=\frac{my_2+ny_1}{m+n}$ to find the y-coordinate.

$-0.4=\frac{3y_2+2(5)}{3+2}$

$-0.4=\frac{3y_2+10}{5}$

$-0.4\times 5=3y_2+10$

$-2-10=3y_2$

$-12=3y_2$

$-4=y_2$

The coordinates of B are (10,-4)

QUESTION 2.

If point D divides CD in the ratio 4 : 5.

Then the coordinates of D are:

$(\frac{4(10)+5(3.6)}{4+5}, \frac{4(-4)+5(-0.4)}{4+5})$

$(\frac{58}{9}, \frac{-18}{9})$

The coordinates of D are $(\frac{58}{9}, -2)$