Question

given jl with J(-9, -5) and L(5,16), if K lies on JL and partitions it such that the ratio of JK to KL is 2:5, find the coordinates of K

Answer 1

Answer:

The coordinates of K is (-5,1)

Step-by-step explanation:

Given

$J = (-9,-5)$

$L = (5,16)$

$JK:KL = 2:5$

Required

Determine K

Using Line ratio formula;

We have:

$K(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Where

$(x_1,y_1) = (-9,-5)$

$(x_2,y_2) = (5,16)$

$m:n = 2:5$

So; we have:

$K(x,y) = (\frac{2 * 5 + 5 * -9}{2+5},\frac{2 * 16 + 5 * -5}{2+5})$

$K(x,y) = (\frac{10 -45}{7},\frac{32 -25}{7})$

$K(x,y) = (\frac{-35}{7},\frac{7}{7})$

$K(x,y) = (-5,1)$