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We are looking the coordinate that divides that segment into a 7/3 ratio.  If we are dividing that segment and looking for a particular coordinate, we must first divide the segment into 7+3 segmments, or 10 equal length segments.  When we plot point L on the segment in a 7/3 ratio, notice that L is 7/10 of the way from J to K.  That ratio is k, found by writing the numerator of our ratio over the sum of the numerator and denominator.  Our k then is 7 over 7+3, so k = 7/10.  Now we will find the rise and the run (aka the slope) of the line.  [tex]m= \frac{-20-10}{5-(-25)} = \frac{-30}{30} [/tex].  We have a rise value of -30 and a run value of 30.  The point L's coordinate are found in this formula: [tex](x,y)=( x_{1}+k(run), y_{1} +k(rise))[/tex].  x1 and y1 are found in the first coordinate, point J (-25, 10).  Filling in accordingly, we have [tex](x,y)=(-25+ \frac{7}{10}(30),10+ \frac{7}{10}(-30)) [/tex] which simplifies to [tex](x,y)=(-25+21,10-21)[/tex].  Those coordinates then of L are (-4, -11)

Answer:  The y co-ordinate of the point L is -11.

Step-by-step explanation:  Given that the co-ordinates of the endpoints of the line segment JK are J(–25, 10) and K(5, –20).

We are to find the y co-ordinate of he point L that divides the line segment JK in the ratio 7 : 3.

We know that

the co-ordinates of a point that divides the line segment with endpoints (a, b) and (c, d) in the ratio m : n are given by

[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right)\\\\\\\Rightarrow \textup{y co-ordinate}=\dfrac{md+nb}{m+n}.[/tex]

Therefore, the y co-ordinate of the point L will be

[tex]y=\dfrac{7\times (-20)+3\times10}{7+3}=\dfrac{-140+30}{10}=\dfrac{-110}{10}=-11.[/tex]

Thus, the y co-ordinate of the point L is -11.

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