Question

In the figure, the midpoints of the large quadrilateral are joined to form the small quadrilateral within:

i. Find the coordinates of the fourth vertex of the smaller quadrilateral.

ii. Find the coordinates of the other three vertices of the larger quadrilateral.

Answer 1

i. Midpoint of AD is S

\(\frac{2+x}{2}=3\)

\(\frac{1+y}{2}=3\)

2 + x = 6

1 + y = 6

x = 4

y = 5

D(4,5)

Midpoint of CD is R

\(\frac{4+x}{2}=3\)

\(\frac{5+y}{2}=6\)

x = 12 - 4

y = 12 - 5

x = 8

y = 7

C(8,7)

Midpoint of BC is Q

\(\frac{8+x}{2}=9\)

\(\frac{7+y}{2}=5\)

x = 18 - 8

y = 10 - 7

x = 10

y = 3

B(10,3)

Midpoint of AB is P

\(x=\frac{2+10}{2}=\frac{12}{2}=6\)

\(y=\frac{1+3}{2}=\frac{4}{2}=2\)

P(6,2)

Coordinate of the fourth vertex of smaller quadrilateral -(6, 2)

ii. Coordinates of other three vertices of the bigger quadrilateral (10, 3),(8, 7),(4, 5)