Question

What is the y-coordinate of the point that divides the

directed line segment from J to k into a ratio of 5:1?

75(7,2)

+

+

+

+

y =

(v2 - y) + va

1 2 3 4 5 6 7 8 9 10 11 x

O

O O

O

J (1,-10)

Answer 1

Answer:

y-coordinate = 0

Step-by-step explanation:

Consider the below diagram attached with this question.

Section formula:

If a point divides a line segment in m:n whose end points are $(x_1,y_1)$ and $(x_2,y_2)$, then the coordinates of that point are

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

From the below graph it is clear that the coordinates of end points are J(1,-10) and K(7,2). A point divides the line JK is 5:1.

Using section formula, the coordinates of that point are

$(\frac{(5)(7)+(1)(1)}{5+1},\frac{(5)(2)+(1)(-10)}{5+1})$

$(\frac{35+1}{6},\frac{10-10}{6})$

$(\frac{36}{6},\frac{0}{6})$

$(6,0)$

Therefore, the y-coordinate of the point that divides the directed line segment from J to k into a ratio of 5:1 is 0.

Answer 2

The y coordinate of the point that divides the directed line segment from J to k into a ratio of 5:1 is 0.

What is a line segment?

A line segment is a line joining two points. If a point O(x, y) divides line AB with endpoints at A(x₁, y₁) and B(x₂, y₂) in the ration n:m, the coordinates are at:

$x=\frac{n}{n+m}(x_2-x_1)+x_1 \\\\y=\frac{n}{n+m}y_2-y_1)+y_1$

Given that line segment JK is at J(1, -10) and K(7, 2). It is divided by point (x, y) in the ratio 5:1, hence:

$y=\frac{5}{5+1}(2-(-10)) +(-10)\\ \\y=0$

The y coordinate of the point that divides the directed line segment from J to k into a ratio of 5:1 is 0.

Find out more on line segment at: https://brainly.com/question/18315903