Q:

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 . If point D divides in the ratio 4 : 5, the coordinates of point D are .Reset Next

Accepted Solution

A:
Answer:Point B is (10 , -4)Point D is (10/9 , 1)Step-by-step explanation:* Lets revise the rule of the point which divides of a line segment in  a ratio- If point (x , y) divides the line segment AB, where A is (x1 , y1) and  B is (x2 , y2) in the ratio m1 : m2∴ x = [m2(x1) + m1(x2)]/(m1 + m2)∴ y = [m2(y1) + m1(y2)]/(m1 + m2)* Now lets solve the problem- Point C (3.6 , -0.4) divides AB in the ratio 3 : 2, where A is (-6 , 5)# x = 3.6 , y = -0.4# A is (x1 , y1) , B is (x2 , y2)∴ x1 = -6 , y1 = 5∵ m1 : m2 = 3 : 2- Substitute these values in the rule ∵ x = [m2(x1) + m1(x2)]/(m1 + m2)∴ 3.6 = [2(-6) + 3(x2)]/(3 + 2) ∴ 3.6  = [-12 + 3x2]/5 ⇒ multiply both sides by 5 ∴ 18 = -12 + 3x2 ⇒ add 12 to both sides∴ 30 = 3x2 ⇒ divide both sides by 3∴ 10 = x2* The x-coordinate of B is 10∵ y = [m2(y1) + m1(y2)]/(m1 + m2)∴ -0.4 = [2(5) + 3(y2)]/(3 + 2)∴ -0.4 = [10 + 3y]/5 ⇒ multiply both sides by 5∴ -2 = 10 + 3y2 ⇒ subtract 10 from both sides∴ -12 = 3x2 ⇒ divide both sides by 3∴ -4 = y2* The y-coordinate of B is -4∴ Point B is (10 , -4)- Point D divides AB in the ratio 4 : 5 where A (-6 , 5) and B (10 , -4)- To find the coordinates of point D use the same rule above# D is (x , y)# A is (x1 , y1) and B is (x2 , y2)# m1 : m2 is 4 : 5∵ x1 = -6 and y1 = 5∵ x2 = 10 and y2 = -4∵ m1 = 4 and m2 = 5- Substitute these values in the rule∵ x = [m2(x1) + m1(x2)]/(m1 + m2)∴ x = [5(-6) + 4(10)]/(4 + 5) ⇒ multiply the numbers∴ x = [-30 + 40]/9 ⇒ add∴ x = [10]/9 ⇒ Divide∴ x = 10/9* The x-coordinate of D is 10/9∵ y = [m2(y1) + m1(y2)]/(m1 + m2)∴ y = [5(5) + 4(-4)]/(5 + 4) ⇒ multiply the numbers∴ y = [25 + -16]/9 ⇒ add∴ y = [9]/9 ⇒ Divide∴ y = 1* The y-coordinate of point D is 1∴ Point D is (10/9 , 1)