**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**+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**+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 )

CPhill
Feb 1, 2018