The y-coordinate of the point that divides the directed line segment from J to K into a ratio of [tex]5:1[/tex] is [tex]\boxed0.[/tex]
Further explanation:
The coordinates of point that divides the line segment into [tex]m:n[/tex] 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:
Explanation:
The coordinate of point J is [tex]\left( { 1,-10}\right)[/tex]
The coordinate of point K is [tex]\left( { 7,2} \right)[/tex]
Consider the point that divides the line segment into [tex]5:1[/tex] ratio as [tex]P\left( {x,y} \right).[/tex]
The coordinates of point that divides the line segment into [tex]5:1[/tex] ratio can be calculated as follows,
[tex]\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}[/tex]
The y-coordinate of the point that divides the directed line segment from J to K into a ratio of [tex]5:1[/tex] is [tex]\boxed0.[/tex]
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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.
