Co-ordinate Geometry?

Question

Find the coordinates of the point which divides the interval joining C (-6,-13) and D (-7,14) in the ratio 1:1.

Answer 1

Let P be the point which divides the interval joining C (-6,-13) and D (-7,14) in the ratio 1:1

let the coordinates of P be (x,y)

now, since the ratio is 1:1,

use section formula ( or mid pt theorem as ratio is 1:1)

x= (-6)+(-7)/1+1
x= -6.5

similarly for the y coordinate

y= -13+14/1+1
y=1/2 or 0.5

Answer
therefore the point P(-6.5,0.5) divides the interval joining C (-6,-13) and D (-7,14) in the ratio 1:1.

Answer 2

Divides in the ratio 1 : 1 essentially means that we must find the mid point. Use this theory:

If a point P(x, y) divides a line segment joining points A(x1, y1) and B(x2, y2) in a ratio m : n internally, Then,

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

Here,
x1 = -6
x2 = -7
y1 = -13
y2 = 14
m = 1 = n

Let the point dividing the line segment be P whose co-ordinates are (x, y)

Now find x and y with the given formula and thereby the co-ordinates of P.

x = (-7 - 6)/2 = -13/2
y = (14 - 13)/2 = 1/2

The coordinates of P are (-13/2, 1/2)


There is another way of doing this. It is easier.
If a point P(x, y) divides a line segment joining points A(x1, y1) and B(x2, y2) in a ratio 1 : 1 internally, Then,

x = (x2 + x1)/2
y = (y2 + y1)/2

because m = 1, n = 1

Answer 3

P(x,y) = ( (1/2)*(x1+x2) , (1/2)*(y1+y2) )
= ( (1/2)*(-6-7) , (1/2)*(-13+14) )
= (1/2)*(-13) , (1/2)*(1) )
= ( (-13/2) , (1/2) )

Answer 4

let M be the coordinate

M[(-6-7)/2 , (-13+14)/2 ]
M(-13/2,1/2)#

Answer 5

this is just a fancy way of asking you to find the midpoint.
using the midpoint theorem, you get (-6.5, .5)