Question

What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3?

Answer 1

The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3 is $\boxed5.$ Option (c) is correct.

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 $\left( { - 3,1} \right)$

The coordinate of point K is $\left( { - 8,11} \right)$

Consider the point that divides the line segment into $2:3$ ratio as $P\left( {x,y} \right).$

The coordinates of point that divides the line segment into $2:3$ ratio can be calculated as follows,

$\begin{aligned}{\text{Coordinates of P}} &= \left( {\frac{{3\left( { - 3} \right) + 2\left( { - 8} \right)}}{{2 + 3}},\frac{{3\left( 1 \right) + 2\left( {11} \right)}}{{2 + 3}}} \right)\\&= \left( {\frac{{ - 9 - 16}}{5},\frac{{3 + 22}}{5}} \right)\\&= \left( {\frac{{ - 25}}{5},\frac{{25}}{5}} \right)\\&= \left( { - 5,5} \right)\\\end{aligned}$

The y-coordinate of the point that divides the directed line segment from J to K into a ratio of $2:3$ is $\boxed5$. Option (c) is correct.

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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 2

Answer:

C. 5

Step-by-step explanation:

We will use section formula when some point divides segment any initially in the ratio m:n.  

$[x=\frac{m*x_2+n*x_1}{m+n},y=\frac{m*y_2+n*y_1}{m+n}]$

Let us substitute coordinates of our given points and m=2 and n=3 in section formula.

$[x=\frac{2*(-8)+3*(-3)}{2+3},y=\frac{2*(11)+3*(1)}{2+3}]$

$[x=\frac{-16-9}{5},y=\frac{22+3}{5}]$

$[x=\frac{-25}{5},y=\frac{25}{5}]$

$[x=-5,y=5]$

We can see that the point (-5, 5) divides the directed line segment from J to K into a ratio of 2:3. Therefore, y-coordinate of the point is 5 and potion C is the correct choice.