Exercise Midpoint

1.     Refer to the Cartesian Plane as shown and find the coordinates of thr midpoint of the line

a)     PQ

b)    QR

1.     Find the coordinates of the midpoint of the straight line joining point P (-2, 2) and point Q (4 ,6).

Solution

The coordinates of the midpoint of the line PQ are ( 1, 4)

1.     Refer to the Cartesian plane as shown and find the coordinates of the midpoint of the straight line joining

a)     P and F                                                                              

b)    H and J

c)     D and  I

d)    E and F

e)     G and H

f)      I and J

1.     Find the coordinates of the midpoint of the line which joins the following pairs of points.

a)     P (2, 5) and Q (8, 5)

b)    M (5, -2) and M (-1, -2)

c)     J (3, -4) and K (3, 2)

d)    A (-4 ,1) and B (-4,-3)

2.     Refer to the Cartesian plane as shown and find the coordinates of the midpoint of the straight line joining

a)     R and Q

b)    T and S

c)     T and U

d)    S and Q

1.     Find the coordinates of the midpoint of the line which joins the following pairs of  points

a)     P (6, 1) and Q ( 2,7)

b)    M (3, 4) and N (-1, 6)

c)     J (2, 5) and K (6, 1)

d)    A (-3, 2) and B (-1, -8)

2.     Given that ( 2, p) is the midpoint of the straight  line joining the points ( 1, 8) and (3, -2), find the value of p

3.     Given that (4 ,3) is the midpoint of the straight line joining the points (k, -1) and (2, 7), find value of k

4.     PQRS is the rhombus. Given that the coordinates of P, Q and R are (-3, 2), (1, 4) and (5, 2) respectively.

a)     Find the coordinates of S

b)    Find the coordinates of midpoint of all the sides of the rhombus.

c)     What the shape of the straight lines which  join all the midpoint?

SOLUTION

           1.

a)    The coordinates of the midpoint of the line PQ are (3, 4).

b)    The coordinates of the midpoint of the line QR are ( 5, 1).

2.  The coordinates of the midpoint of the line PQ are ( 1, 4)

2.   a) ( 0, 4)    b)(-1, 1)

c) (-2, -3)   d)(2, 1)

e) (-3, 0)    f)(1, -1)

      4.  a)(5,5)    b)(2, -2)

           c) (3, -1)  d)(-4, -1)

      5. a) (-1, 3)  b) ( 3, 1)

           c) ( -2, 0) d) (3, 4)

      6. a) (4, 4)  b) ( 1, 5)

        c) ( 4, -2 )  d) ( -2 , -3 )

      7. P = 3

     8. K = 6

     9.  a) ( 1, 0)

          b) (-1, 3), (3 , 3),(3, 1),(-1,1)

          c) Rectangle