Geom_CQA1_20-21 Question: 1-5
The endpoints of MN are located at M (-4, 4) and N (2,-2). What are the coordinates of the point P that divides MN such that MP : PN is equal to 2: 1?
(-3.5, 2.5)
(-2,2)
(-1, 1)
(0,0)

The coordinates of the point P is (0,0)

Step-by-step explanation:

Here, we want to find the coordinates of point P which divides the segment MN in the ratio 2 to 1.

Mathematically, what we shall use here is the internal division formula;

The internal division formula is given as follows;

(x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)

From the question;

x1 = -4

x2 = 2

y1 = 4

y2 = -2

m = 2

n = 1

By substituting, we have;

(1(-4) + 2)2))/(1 + 2) , (1(4) + 2(-2))/(1+2)

= (-4 + 4)/3 , (4-4)/3

= (0,0)

Step-by-step explanation:

Given:

(y/y - 4) - (4/y + 4) = 32/y^2 - 16

Note y^2 - 16 = (y - 4 ) × (y + 4)

Multiplying the equation; both sides by y^2 - 16,

y (y + 4) - (4(y - 4)) = 32

y^2 + 4y - 4y + 16 = 32

y^2 = 32 - 16

Squaring both sides,

y = sqrt(16)

= 4