Question

ine segment XY has endpoints X(–10, –1) and Y(5, 15). To find the y-coordinate of the point that divides the directed line segment in a 5:3 ratio, the formula y = (y2 – y1) + y1 was used to find that y = (15 – (–1)) + (–1). Therefore, the y-coordinate of the point that divides XY into a 5:3 ratio is

Answer 1

Answer:-coordinate of the point that divides the directed line segment in a 5:3 ratio is 9.

Explanation:

Given : Line segment XY has endpoints X(–10, –1) and Y(5, 15) and divides the directed line segment in a 5:3 ratio.

To find : y-coordinate of the point that divides the directed line segment in a 5:3 ratio.

Solution : We have a line segment XY with ends points X(–10, –1) and Y(5, 15).

and divided by 5: 3 ratio.

`x_(1) =-10`,
`x_(2) = 5`,

`y_(1) = -1`,
`y_(2) = 15`.

By section formula : Let P divide line XY in ration m : n , coordinates of P (x,y)

P =(
`((mx_(2) + nx_(1)))/(m+n)` ,
`((my_(2) + ny_(1)))/(m+n)`).

y- coordinate =
`((my_(2) + ny_(1)))/(m+n)`.

Plugging values , m= 5 , n = 3

y- coordinate =
`((5(15) + 3(-1)))/(5+3)`.

y- coordinate =
`(75-3)/(8)`.

y- coordinate = 9.

Therefore , y-coordinate of the point that divides the directed line segment in a 5:3 ratio is 9.

Answer 2

X=(-10,-1)=(Xx,Yx)→Xx=-10, Yx=-1
Y=(5,15)=(Xy,Yy)→Xy=5,Yy=15
y=?
ratio=5:3→r=5/3
y=(Yx+rYy) / (1+r)
y=[-1+(5/3)15] / (1+5/3)
y=[-1+(5*15)/3] / [(3+5)/3]
y=(-1+75/3) / (8/3)
y=(-1+25) / (8/3)
y=(24) / (8/3)
y=24*(3/8)
y=72/8
y=9

Asnwer: The y-coordinate of the point that divides the directed line segment XY in a 5:3 ratio is y=9