# 100 POINTS // ASAP A point Q on a segment with endpoints A (2, −1) and C (4, 2) partitions the segment

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.

## This Post Has 5 Comments

1. itsstaytay200 says:

point q: (3.6, 1.4)

step-by-step explanation:

when you need to find a point between 2 points, you can work with "x" and with "y" separately:

point a: (2, -1)

point c: (4, 2)

distance in x: (4-2) = 2

distance in y: ()) = 3

the point q partitions the segment in 4: 1, from that you can divide the segment in 5 parts.

each part in x = 2/5 = 0.4

each part in y = 3/5 = 0.6

i will assume that the 4 parts are from a to q (because it isnt specified in the problem)

q: point a + 4 parts:

point q: (2, -1) +(0.4*4, 0.6*4) = (3.6, 1,4)

2. joejoefofana says:

Q=(3.6,1.4)

Step By Step:

A point Q on a segment with endpoints A (2, −1) and C (4, 2) partitions the segment in a 4:1 ratio.

A=(x_1,y_1)=(2,-1)

B=(x_2,y_2)=(4,2)

m:n = 4:1

Let (x,y) be the coordinates of Q

Section formula : x=mx_2+nx_1/m+n, y=my_2+ny_1/m+n

Substitute the values in the formula:

x=4(4)+2/4+1, y=4(2)-1/4+1

x=18/5,y=7/5

x=3.6, y=1.4

Hence Q=(3.6,1.4)

3. aklilrodowx1q5 says:

Q = (2, 7/5)

Step-by-step explanation:

Please see attached image for step-by-step explanation

$A point Q on a segment with endpoints A (2, −1) and C (4, 2) partitions the segment in a 4:1 ratio.$

4. manoli5874 says:

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 🙂

5. isalybeaudion2205 says:

( 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