Question

M is the midpoint of JK. The coordinates of J are (6, 3) and the coordinates of M are (-3, 4), find the coordinates of K.

Answer 1

Use the midpoint formula"
http://geometry.jdeer.com/Images/c1/midpoint%20formula.gif

Answer 2

the coordinates of the midpoint (c) can be find by this formula
\[c = [ \frac{ mx_{1} + nx_{2} }{ m +n } , \frac{ my_{1} + ny_{2} }{ m + n } ]\]
where
where x1 , y1 will be the coordinates of the point J and x2 and y2 will be the coordinates of point K

and m and n is the ratio between the distance between JM and MK

got it so far ?

Answer 3

yea im understanding what your doing :)

Answer 4

since the M is the midpoint of JK , the ratio of JM to MK will be 1 ( because JM =MK)
then
n= 1 and m = 1
then we can simplify the equation in to
\[c = [\frac{ x_{1} + x_{2} }{ 2 } , \frac{ y_{1} +y_{2} }{ 2 } ]\]
ok ?

Answer 5

and we already know the coordinates of c ,therefor...
\[( -3 , 4 ) = [ \frac{ x_{1} + x_{2} }{ 2} , \frac{ y_{1} + y_{2} }{ 2 } ]\]

we also know the coordinates of J which is ( 6 , 3 ) represent by x1 and y1 , therefor
\[( - 3 , 4) = [\frac{ 6 + x_{2} }{ 2 } , \frac{ 3 + y_{2} }{ 2 } ]\]
now we can get 2 seperate equations from them

Answer 6

still following

Answer 7

considering the x coordinates
-3 = ( 6 + x2) /2
-6 = 6 + x2 ----(1)
considering the y coordinates
4 = ( 3 + y2) /2
8 = 3 + Y2 ----(2)

using (1) and (2) u can find the coordinates of the point K

hope this will help ya!!

Answer 8

did u got it or did i make it a mess ? :)

Answer 9

yea K =5,6 :)

Answer 10

is K = 5 , 6 is the given answer ?

Answer 11

thats what i got from it (5,6)

Answer 12

"thats what i got from it (5,6)"
"from it" u mean wt ?
the equation i wrote or something else ?

Answer 13

thats what i got as the answer from the equation you set up for me

Answer 14

mmm.... i think u need look twice...
u got the x coordinate as 5 by solving
-6 = 6 + x2
and y coordinate as 6 by solving
8 = 3 + Y2
try to solve them again.......

Answer 15

now im confised lol

Answer 16

ok....
lets c where did u got it wrong...
can u pls tell me the steps u follow to get x coordinates as 5 ?

Answer 17

its ok, dont worry about it. thanks for trying, maybe its just me being tired

Answer 18

u r welcome !! :)