MATH SOLVE

3 months ago

Q:
# The location of point J is (-5,4). The location of point M is (10,-1). Find the location of points K and L. Point K is 2/5 of the way from J to M and point L is 4/5 of the way from J to M

Accepted Solution

A:

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)