100 POINTS // ASAP A point Q on a segment with endpoints A (2, −1) and C (4, 2) partitions the segment in a 4:1 ratio. Find Q. You must show all work to receive credit.

Q = (18/5, 7/5)

Step-by-step explanation:

Given:

A(2, -1)

C(4, 2 )

a:b = 4:1

If  Q(Xq, Yq) divides a line segment from A(X1, Y1) to C(X2, Y2) in the ratio of a:b then

Xq = X1 + ( a / (a + b) ) * (X2 - X1)

Yq = Y1 + ( a / (a + b) ) * (Y2 - Y1)

Xq = 2 + (4 / (4+1)) * (4 - 2) = 18/5

Yq = -1 + (4 / (4+1)) * (2 - (-1)) = 7/5

therefore Q = (18/5, 7/5)

Hope it helps and have fun in maths :-)

( 3 3/5 , 1 2/5)

Step-by-step explanation:

Q is 4/5 of the distance from A to C

The x distance  between A and C is 4-2 = 2

We want 4/5 of that 4/5 (2) = 8/5

Add that to 2

2 + 8/5 = 10/5 + 8/5 = 18/5 = 3 3/5

The y distance  between A and C is 2 --1 = 3

We want 4/5 of that 4/5 (3) = 12/5

Add that to -1

-1 + 12/5 = -5/5 + 12/5 =7/5 =1 2/5

The distance 4/5 of the way from A to C is ( 3 3/5 , 1 2/5)

7

step-by-step explanation: