Question

Find the point, M, that divides segment AB into a ratio of 5:6 if A is at (0,22) and B is at (11,0).

Answer 1

Answer:

The coordinates of point M is (10,6).

Step-by-step explanation:

Given:

The point, M, that divides segment AB into a ratio of 5:6

A is at (0, 22)

B is at (11, 0)

Let the coordinates of the point M is (x,y)

And m=5 and n = 6

Now apply the formula of line division:

x= (m.x2 + n.x1)/(m + n)

y = (m.y2 + n.y1)/(m + n)

By substituton, we have

x= (5×22+6×0)/(5+6)

x = (110 + 0)/11

x = 110/11

x = 10

Similarly

y = (5×0+6×11)/(5 + 6)

y = (0 + 66)/11

y = 66/11

y = 6

x=10 , y=6

So the coordinates of point M is (10,6).

Answer 2

Answer:

(5,12)

Step-by-step explanation:

The co-ordinates of point M is

When provided with points A(x1, y1) and B(x2,y2) then to find the coordinates of the points that divide the line segment AB internally we use the formula

$X=\frac {mx1+nx2}{m+n} and y=\frac {my1+ny2}{m+n}$

Similarly, for the same points but when it’s divided externally we use the formula

$X=\frac {mx1-nx2}{m-n} and y=\frac {my1-ny2}{m-n}$

For this case, we use the first formula

M=5 and n=6 hence m+n=11

Total ratio is 5+6=11

Difference in x direction=11-0=11 points

Difference in y direction=0-22=-22 points

Point M=5/11(11, -22)+ point A

Point M=(5,-10)+(0+22)=(5,12)