Answer:
The location of point K is (1 , 2)
The location of point L is (7 , 0)
Step-by-step explanation:
* Lets revise how to find the location of a point between two points
- If point (x , y) is between two points (x1 , y1) , (x2 , y2) at a ratio
m1 from (x1 , y1) and m2 from (x2 , y2)
∴ x = [x1(m2) + x2(m1)]/(m1 + m2)
∴ y = [y1(m2) + y2(m1)]/(m1 + m2)
* Now lets solve the problem
- Point J is (-5 , 4) and point M is (10 , -1)
∵ Point K is 2/5 of JM
∴ m1 = 2 ⇒ ratio from K to J
∴ m2 = 5 - 2 = 3 ⇒ ratio from K to M
∴ x = [(-5)(3) + (10)(2)]/(2 + 3) = [-15 + 20]/5 = 5/5 = 1
∴ y = [(4)(3) + (-1)(2)]/(2 + 3) = [12 + -2]/5 = 10/5 = 2
* The location of point K is (1 , 2)
∵ Point L is 4/5 of JM
∴ m1 = 4 ⇒ ratio from K to J
∴ m2 = 5 - 4 = 1 ⇒ ratio from K to M
∴ x = [(-5)(1) + (10)(4)]/(2 + 3) = [-5 + 40]/5 = 35/5 = 7
∴ y = [(4)(1) + (-1)(4)]/(2 + 3) = [4 + -4]/5 = 0/5 = 0
* The location of point L is (7 , 0)
