Answer:
Point B is (10 , -4)
Point D is (10/9 , 1)
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)