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1. find the midpoint of the segment connecting the points (a,b) to (5a,-7b). (Hint: answer will contain variables a and b.)

2.Find the coordinates of point P which divides the directed line segment AB with coordinates A(5,-2) and B(9,6) in the ratio 3:1.

3.  Point C is on the directed line segment from points A(-11,4) to point B(-1,-6) and divides the segment in the ratio 2 to 3. Find the coordinates of C.

 

(SHOW WORK AND EXPLAIN)

Mathisfornerds  Feb 1, 2018
 #1
avatar+7339 
+3

1.

 

midpoint of  (a, b)  and  (5a, -7b)   =   ( [a + 5a]/2 ,  [b + -7b]/2 )   =   ( 6a/2 ,  -6b/2 )   =   ( 3a, -3b )

hectictar  Feb 1, 2018
 #2
avatar+92808 
+2

1. find the midpoint of the segment connecting the points (a,b) to (5a,-7b). (Hint: answer will contain variables a and b.)

 

Mid-point formula  :   [  add x coordinates / 2 , add y coordinates / 2  ]

 

So we have

 

[   ( a + 5a) / 2, ( b - 7b) / 2 ]  =

 

[ (6a)/2, (-6b)/2]  =

 

[  3a,  -3b ]

 

 

2..Find the coordinates of point P which divides the directed line segment AB with coordinates A(5,-2) and B(9,6) in the ratio 3:1.

 

A ratio of 3:1  means that we are dividing the distance between these two points into 4 equal parts

 

We are looking for a point P that is    3/4  of the distance from  A  and B

 

So  we have

 

[  5  +  ( 9 - 5)(3/4)  ,  -2 +  ( 6 - - 2) (3/4) ]  =

 

[  5  + (4)(3/4) ,    -2  +  (8)(3/4)  ]  =

 

[ 5 + 3,   -2  + 6 ]  =

 

( 8, 4 )

 

 

 

 

3.  Point C is on the directed line segment from points A(-11,4) to point B(-1,-6) and divides the segment in the ratio 2 to 3. Find the coordinates of C.

 

Like the last one, a ratio of 2 : 3  divides the distance  between these points into 5 equal parts

and we are looking for  point C that is 2/5 the distance from A to B

 

So   we have

 

[  -11 +  (-1 - -11)(2/5) ,  4 + ( -6 - 4) (2/5)  ]  =

 

[  -11 +  (10)(2/5) ,  4 + (-10)(2/5) ] =

 

[ -11 + 4 , 4 + -4 ]  =

 

( - 7, 0 )

 

 

cool cool cool

CPhill  Feb 1, 2018

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