The endpoints of AB are A(1,4) and B(6,-1).

Question

If point C divides AB in the ratio 2 : 3, the coordinates of point C are (___,___).

If point D divides AC in the ratio 3 : 2, the coordinates of point D are (___,___).

Answer 1

2/5 of 5 = 2 add 2 to 1 to get 3 for the x coordinate

2/5 of -5 = -2. add -2 to 4 to get 2 for the y coordinate

(3,2) is C

AC is from (1,4) to (3,2) where x goes up 2 and y goes down 2

dividing it in 3:2 means 3/5 from (1,4). 3/5x2 = 6/5 add to 1 to get 16/5 for the x coordinate of D

3/5 x-2 = -6/5 add that to 4 to get -6/5 + 20/5 = 14/5 for the y coordinate of D

D = (16/5, 14/5) = (3.2, 2.8)

Answer 2

Determine x-coordinate of C as 2/5 of the way between x-coordinate of A (1) and x-coordinate of B (6)

2/5(6-1) + 1 = 3

Determine y-coordinate of C as 2/5 of the way between y-coordinate of A (4) and y-coordinate of B (-1)

2/5(-1-4) + 4 = 2

C(3,2)

Determine x-coordinate of D as 3/5 of the way between x-coordinate of A (1) and x-coordinate of C (3)

3/5(3-1) + 1 = 11/5

Determine y-coordinate of D as 3/5 of the way between y-coordinate of A (4) and y-coordinate of C (2)

3/5(2-4) + 4 = 14/5

D(11/5,14/5)