Find the area of the triangle defined by the points \( (2,3),(-4,3) \) and \( (-6,6) \). 9 16 18 4.5 QUESTION 3 Which shapes have the same area? \[ \text { I. }(1,1),(1,4),(4,4),(4,1) \] II. \( (0,0),(0,-4.5),(-2,0),(-2,-4.5) \) III. \( (4,-3),(2,-5),(6,-5) \) They all have different areas II and III I, II and III I and II

Let's address each question one by one. --- ### **Question 2** **Find the area of the triangle defined by the points \( (2,3), (-4,3) \), and \( (-6,6) \).** **Options:** - 9 - 16 - 18 - 4.5 **Solution:** 1. **Identify the Base and Height:** - Points \( A(2,3) \) and \( B(-4,3) \) lie on the same horizontal line (\( y = 3 \)), so \( AB \) can serve as the base. - Length of base \( AB \): \[ |2 - (-4)| = 6 \text{ units} \] - The height is the vertical distance from point \( C(-6,6) \) to the line \( y = 3 \): \[ 6 - 3 = 3 \text{ units} \] 2. **Calculate the Area:** \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 3 = 9 \] **Answer:** **9** --- ### **Question 3** **Which shapes have the same area?** **Given Shapes:** 1. **I.** Points \( (1,1), (1,4), (4,4), (4,1) \) 2. **II.** Points \( (0,0), (0,-4.5), (-2,0), (-2,-4.5) \) 3. **III.** Points \( (4,-3), (2,-5), (6,-5) \) **Options:** - They all have different areas - II and III - I, II and III - I and II **Solution:** 1. **Shape I:** - This is a rectangle with length and width both equal to 3 units. - **Area:** \( 3 \times 3 = 9 \) 2. **Shape II:** - This is a rectangle with length 2 units and height 4.5 units. - **Area:** \( 2 \times 4.5 = 9 \) 3. **Shape III:** - This is a triangle with a base of 4 units and a height of 2 units. - **Area:** \( \frac{1}{2} \times 4 \times 2 = 4 \) **Conclusion:** - Shapes **I** and **II** both have an area of **9**. - Shape **III** has a different area of **4**. **Answer:** **I and II** ---