Question

The endpoints of JK are J(–25, 10) and K(5, –20). What is the y-coordinate of point L, which divides JK into a 7:3 ratio? a. –16 b.–11 c. –4 d.–1

Answer 1

let's say the point dividing JK is say point P, so the JK segment gets split into two pieces, JP and PK

$\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ J(-25,10)\qquad K(5,-20)\qquad \qquad \stackrel{\textit{ratio from J to K}}{7:3} \\\\\\ \cfrac{J~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~K} = \cfrac{7}{3}\implies \cfrac{J}{K} = \cfrac{7}{3}\implies3J=7K\implies 3(-25,10)=7(5,-20)\\\\[-0.35em] ~\dotfill$

$\bf P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\cfrac{(3\cdot -25)+(7\cdot 5)}{7+3}\quad ,\quad \stackrel{\textit{y-coordinate}}{\cfrac{(3\cdot 10)+(7\cdot -20)}{7+3}}\right) \\\\\\ P=\left( \qquad ,\quad \cfrac{30-140}{10} \right)\implies P=\left(\qquad ,~~\cfrac{-110}{10} \right)\implies P=(\qquad ,\quad -11)$

Answer 2

Answer:

-11

Step-by-step explanation:

J =(–25, 10)

K=(5, –20)

Point L divides JK into a 7:3 ratio

To find the coordinates of L we will use section formula.

Formula : $x=\frac{mx_2+nx_1}{m+n}$ and $y=\frac{my_2+ny_1}{m+n}$

m: n = 7: 3

$(x_1,y_1)=(-25,10)\\(x_2,y_2)=(5,-20)$

Substitute the values

$x=\frac{7(5)+3(-25)}{7+3}$ and $y=\frac{7(-20)+3(10)}{7+3}$

$x=-4$ and $y=-11$

Hence the y coordinate of L is -11