https://file.aiquickdraw.com/mathbot/file/1727075026302k4k0hwt2.jpg

I see the image contains a mathematics question paper with multiple sections (B and C) covering various topics. Here's a breakdown of some key questions:

**Section B:**
1. **Q21:** Plot given points and check if they are collinear.
   Points: (1,3), (-1,-1), (-2,-3)
   
2. **Q22:** Prove that in a parallelogram, the bisectors of any two consecutive angles intersect at a right angle.
   
3. **Q23:** Express \( 1.27 \) in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).

4. **Q24 (OR):** Prove geometric properties related to trapeziums, where \( AB \parallel DC \), and lines are drawn parallel to \( AB \).

5. **Q25:** Calculate the area of a triangle with specific sides.

**Section C:**
1. **Q26:** Solve an equation involving rational numbers \( a \) and \( b \).
   Equation: 
   \[
   \frac{5 + 2\sqrt{3}}{7 + 4\sqrt{3}} = a + b\sqrt{3}
   \]
   Find \( a \) and \( b \).

2. **Q27:** Factorize the expression:
   \[
   2x^2 + y^2 + z^2 - 2 \sqrt{2} yz + 4 \sqrt{2} y z - 8xz
   \]

3. **Q28:** Given \( x + y + z = 9 \) and \( x^2 + y^2 + z^2 = 35 \), find \( x^3 + y^3 + z^3 - 3xyz \).

4. **Q29:** Geometry proof involving a figure and a property related to equality of segments.

Let me know if you'd like me to work on any specific question or need detailed solutions for any problem from the paper.

Do you have any questions about this, or would you like to dive into a detailed explanation?

Here are 5 related questions for exploration:
1. How do you prove that points are collinear in a plane using coordinates?
2. What is the significance of angle bisectors intersecting at right angles in parallelograms?
3. How can rationalizing the denominator help in simplifying expressions like in Q26?
4. What strategies can be used to factorize complex polynomial expressions with square roots?
5. What properties of a triangle can be derived from its perimeter and sides?

**Tip:** Always sketch a figure when dealing with geometric proofs—it helps visualize relationships clearly!

The mathematics question paper involves several problems in geometry, algebra, and number theory. Key topics include collinearity, angle bisectors, trapezium properties, rational expressions, and factorization.

Explore solutions to geometry and algebra questions covering trapezium properties, collinearity, rational expressions, and polynomial factorization. The problems are ideal for students in grades 9-11.

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