Question

What are the me and you

Answer 1

Complete question:

What are the x- and y- coordinates of point E, which partitions the directed line segment from $A\:(- 4,\:9) \:to\: B\:(2,\:- 3)$ into a ratio of 1 : 2.

Answer:

(C) (-2,5)

Step-by-step explanation:

$x = (\dfrac{m}{m+n}) (x_2-x_1) + x_1\\\\y = (\dfrac{m}{m+n}) (y_2-y_1) + y_1$

$(x_1,y_1)=(- 4,\:9),(x_2,y_2)=B\:(2,\:- 3)$

m=1, n=2

$x = \left(\dfrac{1}{1+2}\right) (2-(-4)) + (-4)\\=\left(\dfrac{1}{3}\right) (2+4)-4\\=\left(\dfrac{6}{3}\right)-4=2-4\\x=-2$

$y = \left(\dfrac{1}{1+2}\right) (-3-9) + 9\\=\left(\dfrac{1}{3}\right) (-12)+9\\=\left(-\dfrac{12}{3}\right)+9=-4+9\\y=5$

The x- and y-coordinates of the point E is (-2,5)