+1 vote
1) Given segment AB with endpoints A(2x, 4y) and B(10, 22), what is the midpoint?
A) (x+2 ½ , y+5 ½)
B) (2x-10, 4y-11)
C) (x+5, 2y+11)
D) (2x+5, 4y+11)

2) B is the midpoint of AC. A has coordinates (-3, 4) and B has coordinates (-1 ½, 1). Find the coordinates of C.
A) (-4½, 5)
B) (0, -1)
C) (0, -2)
D) (-2¼, 2½)

3)The endpoints of segment EF are E(-2, 3) and F(5, -3). Find the coordinates of the midpoint of EF.
A) (½, 2)
B) (0, 5)
C) (3, 0)
D) (1 ½, 0)

4)Y is the midpoint of segment XZ. The coordinates of X are (2, 4) and of Y are (-1, 1). Find the coordinates of Z.
A) (1, 5)
B) ( 2, -1)
C) (½, 2 ½)
D) (-4, -2)

5) Given segment VW with endpoints V(-2, -6) and W(x+2, y+3), find the coordinates of the midpoint.
A) (x, y-3)
B) (x/2, y/2)
C) (x/2, (y-3)/2)
D) (x-2, y-3)

1) Given segment AB with endpoints A(2x, 4y) and B(10, 22), what the midpoint?

Given A(2x,4y) ; B(10, 22)

Let A( 2x, 4y) = (x1,y1) and  B(10,22) = (x2,y2) say

Mid point = (  (x1+x2) / 2 , (y1+y2) / 2)

Mid point = ( (2x + 10) / 2 , (4y + 22) / 2 )

Disributive property (ab + ac) = a(b+c)

Mid point =  ( 2( x+5 ) / 2 , 2(2y +11) / 2 )

Mid point =  ( (x+5) , (2y +11) )

The option C  is  correct.

2) B is the midpoint of AC. A has coordinates (-3, 4) and B has coordinates (-1 ½, 1). Find the coordinates of C.

Given Midpoint = B( -1 1/2 , 1) ;  one end point A( -3,4)

Let second end point = C( x2,y2)

Let A(-3,4) = ( x1,y1 )

Midpoint = ( (x1+x2)  / 2 ,(y1+y2) / 2 )

( -1 1 /2, 1) = ( (-3+x2) / 2 , (4+y2) / 2 )                          ( 1 1/2 = 3 /2)

( -3 / 2 , 1) =  ( (-3+x2) / 2 , (4+y2) / 2 )

To take each side  first coefficient = first coefficient, second coefficient = second coefficient.

-3 / 2 = (-3+x2) / 2---(1) ; 1 = (4+y2) / 2 -------(2)

Equation (1) and (2) multiply each side by 2

-3*2 / 2 = (-3+x2)*2 / 2 and 1*2 = (4+y2) *2 / 2

-3 = (-3+x2) and 2 = (4+y2)

To take -3 = -3+x2

-3+3 =-3+x2+3

0 =x2

To take 2 = 4+y2

Subtract 4 from each side

2-4 =4+y2-4

-2 = y2

second end point  C( x2,y2) = (0,-2)

The option C  is  correct.

3)The endpoints of segment EF are E(-2, 3) and F(5, -3). Find the coordinates of the midpoint of EF.

Given E( -2,3) ; F(5, -3)

Let  E( -2,3) = (x1,y1) and  F(5, -3) = (x2,y2) say

Mid point = (  (x1+x2) / 2 , (y1+y2) / 2)

Mid point = ( ( -2+5) / 2 , (-3+3) / 2 )

Mid point = ( 3 / 2, 0/2 )

Mid point = ( 3 / 2, 0 )                      (3/2= 1 1/2)

Mid point = ( 1 1 / 2, 0 )

The option  is D correct.

4)Y is the midpoint of segment XZ. The coordinates of X are (2, 4) and of Y are (-1, 1). Find the coordinates of Z

Given Midpoint =Y(-1,1) ;  one end point X(2,4)

Let second end point = Z( x2,y2)

Let X(2,4)= ( x1,y1 )

Midpoint = ( (x1+x2)  / 2 ,(y1+y2) / 2 )

(-1,1) = ( (2+x2) / 2 , (4+y2) / 2 )

To take each side  first coefficient = first coefficient, second coefficient = second coefficient.

-1 = (2+x2) / 2---(1) ; 1 = (4+y2) / 2 -------(2)

Equation (1) and (2) multiply each side by 2

-1*2 / 2 = (2+x2)*2 / 2 and 1*2 = (4+y2) *2 / 2

-2 = (2+x2) and 2 = (4+y2)

To take -2 =2+x2

-2+2 =2+x2+2

0 =x2+4

Subtract 4 from each side

0-4=x2+4-4

-4 = x2

To take 2 = 4+y2

Subtract 4 from each side

2-4 =4+y2-4

-2 = y2

second end point  C( x2,y2) = (-4,-2)

The option D  is  correct.

.

5) Given segment VW with endpoints V(-2, -6) and W(x+2, y+3), find the coordinates of the midpoint.

Given V(-2,-6) ; W(x+2,y+3)

Let V(-2,-6)= (x1,y1) and= W(x+2,y+3) =(x2,y2) say

Mid point = (  (x1+x2) / 2 , (y1+y2) / 2)

Mid point = ( (2+x-2 ) / 2 , (-6+y+3) / 2 )

Mid point =  (x / 2)  , (y-3) / 2 )

The option C  is  correct.

3)The endpoints of segment EF are E(-2, 3) and F(5, -3). Find the coordinates of the midpoint of EF.

Given E( -2,3) ; F(5, -3)

Let  E( -2,3) = (x1,y1) and  F(5, -3) = (x2,y2) say

Mid point = (  (x1+x2) / 2 , (y1+y2) / 2)

Mid point = ( ( -2+5) / 2 , (+3-3) / 2 )

Mid point = ( 3 / 2, 0/2 )

Mid point = ( 3 / 2, 0 )                      (3/2= 1 1/2)

Mid point = ( 1 1 / 2, 0 )

The option  is D correct.

5) Given segment VW with endpoints V(-2, -6) and W(x+2, y+3), find the coordinates of the midpoint.

Given V(-2,-6) ; W(x+2,y+3)

Let V(-2,-6)= (x1,y1) and= W(x+2,y+3) =(x2,y2) say

Mid point = (  (x1+x2) / 2 , (y1+y2) / 2)

Mid point = ( (-2+x+2 ) / 2 , (-6+y+3) / 2 )

Mid point =  (x / 2)  , (y-3) / 2 )

The option C  is  correct.