Question

The endpoints of JK are J(–3,–7) and K(5,9).
What are the coordinates of the following points on JK?
11. point W is(1/4)the distance from J to K.
12. point R is(3/4)the distance from J to K.
13. point P is(1/8)the distance from J to K.​

Answer 1

Given : the end point of JK are J(-3,-7) and K(5,9).

To Find :  the coordinates of the following point on JK?​

point W is(1/4)the distance from J to K.

point R is(3/4)the distance from J to K.

point P is(1/8)the distance from J to K.​

Solution :

W is(1/4)the distance from J to K.

=> JW = JK/4

=> 4JW = JW + WK

=> 3JW = WK

=> JW : WK = 1 : 3

W divided JK in 1 : 3  ratio

J(-3,-7) and K(5,9)

W  =  ( 1 * 5 + 3 (-3) )/ (1 + 3)  , ( 1 * 9  + 3(-7)) / ( 1 + 3)

=> W = (- 1 , - 3)

Similarly

point R is(3/4)the distance from J to K.

=> R divide J to K  in  3 :1  ratio

R = ( 3 * 5 +1 (-3) )/ (3+ 1)  , ( 3 * 9  + 1(-7)) / (3+ 1)

=>R =  ( 3 , 5)

point P is(1/8)the distance from J to K.​

=> R divide J to K  in  1: 7   ratio

J(-3,-7) and K(5,9)

P  =  ( 1 * 5 + 7 (-3) )/ (1 + 7)  , ( 1 * 9  + 7(-7)) / ( 1 + 7)

=> P = (- 2 , - 5)

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