A(2,1),B(6,5),C(10,3),D(8,3) are vertices of quadrilateral ABCD. The points L,M,N and O are the midpoint of AB and BC and CD and DA. Draw quadrilateral by joining points A,B,C and D on the Cartesian?

To draw the quadrilateral ABCD on the Cartesian plane, we first plot the given points A(2,1), B(6,5), C(10,3), and D(8,3).

Next, we find the midpoints of the sides AB, BC, CD, and DA:

Midpoint of AB:
L = ((2+6)/2, (1+5)/2) = (4,3)

Midpoint of BC:
M = ((6+10)/2, (5+3)/2) = (8,4)

Midpoint of CD:
N = ((10+8)/2, (3+3)/2) = (9,3)

Midpoint of DA:
O = ((8+2)/2, (3+1)/2) = (5,2)

Now, we plot the midpoints L, M, N, and O on the Cartesian plane.

Finally, we join the points A, B, C, and D to form the quadrilateral ABCD. The quadrilateral should have sides AB, BC, CD, and DA with midpoints L, M, N, and O respectively.

The final drawing of the quadrilateral ABCD on the Cartesian plane should look like this:

A(2,1) - B(6,5)
| /
| /
| /
| /
| /
D(8,3) - C(10,3)

Step 1: Find the Midpoints of AB, BC, CD, and DA

- Midpoint of AB (L): ((2+6)/2, (1+5)/2) = (4, 3)
- Midpoint of BC (M): ((6+10)/2, (5+3)/2) = (8, 4)
- Midpoint of CD (N): ((10+8)/2, (3+3)/2) = (9, 3)
- Midpoint of DA (O): ((2+8)/2, (1+3)/2) = (5, 2)

Step 2: Join the Points to Draw the Quadrilateral

- Connect points A, B, C, and D to form quadrilateral ABCD.
- Connect points L, M, N, and O to form the midpoints quadrilateral LMON.

Here is the Cartesian plane with the quadrilateral and its midpoints:

```
C(10,3)
/ \
/ \
/ \
/ \
/ \
B(6,5) ------------------ D(8,3)
\ /
\ /
\ /
\ /
\ /
\ /
A(2,1)
```

Midpoint Quadrilateral LMON:

```
N(9,3)
/ \
/ \
/ \
/ \
/ \
L(4,3) ------------------ O(5,2)
\ /
\ /
\ /
\ /
\ /
\ /
M(8,4)
```