The y-coordinate of the point that divides the directed line segment from J to K into a ratio of [tex]2:3[/tex] is [tex]\boxed5[/tex]. Option (c) is correct.
Further explanation:
The coordinates of point that divides the line segment into m:n ratio can be obtained as follows,
[tex]\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)}[/tex]
Given:
The options are as follows,
A. -6
B. -5
C. 5
D. 7
Explanation:
The coordinate of point J is [tex]\left( { - 3,1} \right)[/tex]
The coordinate of point K is [tex]\left( { - 8,11} \right)[/tex]
Consider the point that divides the line segment into [tex]2:3[/tex] ratio as [tex]P\left( {x,y} \right).[/tex]
The coordinates of point that divides the line segment into [tex]2:3[/tex] ratio can be calculated as follows,
[tex]\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}[/tex]
The y-coordinate of the point that divides the directed line segment from J to K into a ratio of [tex]2:3[/tex] is [tex]\boxed5.[/tex] 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.
