1. **Find the gradient between each pair of points given:** Gradient formula between points $(x_1,y_1)$ and $(x_2,y_2)$ is $$ gradient = \frac{y_2 - y_1}{x_2 - x_1} $$ 2. Between A(3,2) and B(6,2): $$ gradient = \frac{2 - 2}{6 - 3} = \frac{0}{3} = 0 $$ 3. Between C(2,0) and D(4,-4): $$ gradient = \frac{-4 - 0}{4 - 2} = \frac{-4}{2} = -2 $$ 4. Between M(-2,0) and N(0,4): $$ gradient = \frac{4 - 0}{0 - (-2)} = \frac{4}{2} = 2 $$ 5. Between X(-4,-1) and Y(-3,-3): $$ gradient = \frac{-3 - (-1)}{-3 - (-4)} = \frac{-3 + 1}{-3 + 4} = \frac{-2}{1} = -2 $$ --- 6. **Find gradients of sides of quadrilateral ABCD where** $A(-2,-1), B(-1,1), C(3,3), D(2,1)$ 7. Gradient of AB: $$ gradient = \frac{1 - (-1)}{-1 - (-2)} = \frac{2}{1} = 2 $$ 8. Gradient of BC: $$ gradient = \frac{3 - 1}{3 - (-1)} = \frac{2}{4} = 0.5 $$ 9. Gradient of CD: $$ gradient = \frac{1 - 3}{2 - 3} = \frac{-2}{-1} = 2 $$ 10. Gradient of DA: $$ gradient = \frac{-1 - 1}{-2 - 2} = \frac{-2}{-4} = 0.5 $$ --- 11. **Is the quadrilateral a parallelogram?** A quadrilateral is a parallelogram if opposite sides have equal gradients. Opposite sides: - AB and CD both have gradient 2 - BC and DA both have gradient 0.5 Since opposite sides have equal gradients, the quadrilateral ABCD is a parallelogram. **Final answers:** - Gradient AB = 2 - Gradient BC = 0.5 - Gradient CD = 2 - Gradient DA = 0.5 - Quadrilateral ABCD is a parallelogram: Yes