Question

Select the correct answer from each drop-down menu.

Answer 1

Answer:

Coordinates of point B are (10,-4)

Coordinates of point D are (3.6,-0.4)

Step-by-step explanation:

1) 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 ____

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

Coordinates of A =$(x_1,y_1)=(-6,5)$

Coordinates of C=(x,y)=(3.6,-0.4)

We will use section formula over here

$x=\frac{mx_2+nx_1}{m+n} , y = \frac{my_2+ny_1}{m+n}$

m:n=3:2

$3.6=\frac{3x_2+2(-6)}{3+2} , -0.4=\frac{3y_2+2(5)}{3+2}3.6 \times 5 = 3x_2-12, -0.4 \times 5 = 3y_2+10\\18+12=3x_2 , -2=3y_2+10\\30=3x_2 , -12=3y_2\\10=x_2, -4=y_2$

Coordinates of B = (10,-4)

2)If point D divides in the ratio 4 : 5, the coordinates of point D are ____

(fraction)

Let the coordinates of D be $(x,y)$

Coordinates of A =$(x_1,y_1)=(-6,5)$

Coordinates of B=$(x_2,y_2)=(10,-4)$

We will use section formula over here

$x=\frac{mx_2+nx_1}{m+n} , y = \frac{my_2+ny_1}{m+n}$

m:n=3:2

$x=\frac{3(10)+2(-6)}{3+2} , y=\frac{3(-4)+2(5)}{3+2}\\x=3.6,y=-0.4$

Coordinates of point B are (10,-4)

Coordinates of point D are (3.6,-0.4)