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`

Answer 2

-11

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=(mx_2+nx_1)/(m+n)` and
`y=(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=(7(5)+3(-25))/(7+3)` and
`y=(7(-20)+3(10))/(7+3)`

`x=-4` and
`y=-11`

Hence the y coordinate of L is -11