Mathematics, 24.12.2019 12:31 lindseyklewis1p56uvi

What is the y-coordinate of the point that divides the directed line segment from j to k into a ratio of 5: 1?

What is the y-coordinate of the point that divides the directed line segment from j to k into a rati

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Answer from: kayleahrayne

Answer-

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

Solution-

Given J (1, -10) and K (7, 2)

Let us assume that, point L divides the directed line segment from J to K into a ratio of 5:1

From the properties of coordinate geometry we know that,

The coordinates of point that divides the line joining (x₁, y₁), (x₂, y₂) in m:n, are

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

Now, putting the respective values,

$=(\dfrac{5\cdot 7+1\cdot 1}{5+1},\dfrac{5\cdot 2+1\cdot (-10)}{5+1})$

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

$=(\dfrac{36}{6},\dfrac{0}{6})$

=(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.

What is the y-coordinate of the point that divides the directed line segment from j to k into a rati

Answer from: stressedmolly632

The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is $\boxed0.$

Further explanation:

The coordinates of point that divides the line segment into m:n ratio can be obtained as follows,

$\boxed{{\text{Coordinates of point}} = \left( {\frac{{m{x_2} + n{x_1}}}{{m + n}},\frac{{m{y_2} + n{y_1}}}{{m + n}}} \right)}$

Given:

Explanation:

The coordinate of point J is $\left( { 1,-10}\right)$

The coordinate of point K is $\left( { 7,2} \right)$

Consider the point that divides the line segment into 5:1 ratio as $P\left( {x,y} \right).$

The coordinates of point that divides the line segment into 5:1 ratio can be calculated as follows,

$\begin{aligned}{\text{Coordinates of P}}&= \left( {\frac{{5\left( 7 \right) + 1\left( 1 \right)}}{{5 + 1}},\frac{{5\left( 2 \right) + 1\left( { - 10} \right)}}{{5 + 1}}} \right)\\&=\left( {\frac{{35 + 1}}{6},\frac{{10 - 10}}{6}} \right)\\&= \left( {\frac{{36}}{6},\frac{0}{6}} \right)\\&= \left( {6,0} \right)\\\end{aligned}$

The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is $\boxed0.$

Learn more:

1. Learn more about inverse of the functionhttps://.

2. Learn more about equation of circle .

3. Learn more about range and domain of the function

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: y-coordinate, point, divides the directed line, line segment, J to K, ratio, 2:3 ratio, -6, coordinates.

Answer from: Quest

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Answer from: Quest

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step-by-step explanation: