Question

Points D, E, and F are collinear and DE:DF= 2/5. Point E is locate at (-3,2), point F is located at (-3,-4). What is the coordinate point of point D?

Answer 1

DE : DF = 2 : 5

So, DE = 2 parts and DF = 5 parts

EF = DF - DE

    = 5 - 2

    = 3 parts

DE : EF = 2 : 3

Let D be (x, y).

Then, the point E divides the line segment DF internally in the ratio 2 : 3.

So, E is $(\frac{2(-3)+3x}{2+3}, \frac{2(-4)+3y}{2+3} )$

$=(\frac{3x-6}{5}, \frac{3y-8}{5} )$

But, it is given that E is (-3, 2).

Therefore,

$\frac{3x-6}{5} = -3 and \frac{3y-8}{5}=2$

3x - 6 = -15 and 3y - 8 = 10

3x = -9 and 3y = 18

x = -3 and y = 6

Hence, D is (-3, 6)