Time to wake up that brain! This crossword’s here to help you refresh your Cartesian Plane knowledge in a fun way.

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Set 1: Cartesian Coordinates & Distance Formula

Duration : 1 hour

Answer the Following Exercise

1. Plot the points (2, 3) and (5, 7) on the Cartesian plane.

2. Identify the quadrant for the point (−4, 6).

3. Find the distance between (1, 2) and (4, 6).

4. Calculate the midpoint between (−3, 5) and (3, −1).

5. A square has corners at (1,1) and (5,1). Find the length of one side.

6. Determine if triangle with points A(0,0), B(3,4), and C(3,0) is right-angled.

7. A circle has diameter endpoints at (−2, 4) and (6, 8). Find the centre and radius.

8. In a coordinate layout, two machines are located at A(2,3) and B(10,15). Calculate the exact distance and suggest shortest cable route.

9. A robotic arm moves from point A(2,5) to point B(10,9). Calculate the linear travel distance of the arm.

10. A CNC machine table has two drill positions at (0,0) and (6,8). What is the diagonal distance between the drills?

Collaborative Activity (Pair Work)

Durations : 20 Minutes

Title: Coordinate Geometry in Real Objects

Instructions:

1. In pairs, choose one technical object around you (e.g. a mechanical tool, electronic device, or classroom equipment).

2. Identify two distinct components within the object.

3. Trace the positions of these two components and represent their locations using coordinates on a Cartesian plane. You may assign your own coordinate system (e.g., origin at the bottom-left of the object).

4. Using the coordinates, calculate:

   • The distance between the two components.

   • The midpoint between them.

5. Record your findings and be prepared to share with the class.

6. DOWNLOAD ACTIVITY SHEETS

📝 Project Task (Instructions):

Duration : 1 Hour

You are required to design an infographic OR a mind map to show real-world applications of the Distance and Midpoint formulas in various fields such as:

• Engineering / Technical fields

• Navigation / Mapping / GPS

• Architecture / Construction

• Robotics / Design

• Sports analytics, etc.

💡 What to include in your infographic or mind map:

1. At least 2 real-world applications for each concept:

   • 2 for Distance formula

   • 2 for Midpoint formula

2. Brief explanation (1-2 sentences) of how each application works.

3. Visual elements (icons, diagrams, color-coding) to enhance clarity and engagement.

4. Must be organized, easy to read, and creatively presented (digital or hand-drawn).

✅ Rubric Pemarkahan (20 Marks Total)

🎯 Tips to Answer

1. You may use tools like Canva, Piktochart, MindMeister, or hand-drawn artwork.

2. Refer to your class notes and real-world examples for inspiration.

Read the following comic strips and identify the applications of equations in engineering.

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Set 2: Equations of Straight Line

Duration : 30 minutes

Answer the Following Exercise

1. Write the equation of a line with slope 2 and y-intercept 3.

2. Form the line equation passing through (0, 5) with slope −1.

3. Find the equation of the line passing through (1, 2) and (3, 6).

4. Convert the line (y = 2x + 3) into general form.

5. A line has x-intercept 4 and y-intercept −2. Write in intercept form.

6. Determine whether the point (4,11) lies on the line (y = 2x + 3).

7. A line passes through (2,−3) and is parallel to (y = 4x + 1). Find its equation.

8. Find the equation of a line perpendicular to (y = x − 4) and passing through (6,2).

9. In an automated conveyor design, the belt moves in a straight line from point (2,3) to (8,9). Find the equation of the belt’s path.

10. A part on an assembly line travels in a straight line and reaches the x-axis at x = 6 and y-axis at y = 4. Form the equation using intercept form.

Title: Exploring Straight Lines in the Real World

Duration: 1 Hour

Group: Pair work (2 students)

Instructions:

🧠 Task Description:

Work together in pairs to observe your surroundings (classroom, lab, campus, etc.) and identify an object or structure that contains or follows a straight line (e.g., edge of a whiteboard, window frame, floor tiles, railing, conveyor path, etc.).

Then:

1. 1. Take a photo or draw the object and label at least two key points on the line.

   2. Use an appropriate method (e.g., slope-intercept, two-point form, or intercept form) to determine the equation of the straight line.

   3. Explain briefly which method you used and why.

   4. Present your findings in a short report or visual presentation (digital or hand-drawn).

📊 Assessment Rubric (Total: 20 marks)

Rearrange the sentence to determine the properties of parallel and perpendicular lines.

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Set 3 : Parallel and Perpendicular Lines

Duration : 30 minutes

Answer the Following Exercise

1. Write the equation of a line with slope 2 and y-intercept 3.

2. Proof that the two lines y - 4x + 8 = 0 and 3y – 12x = 1 are parallel.

3. Find the gradient of line perpendicular to y = -8x + 3.

4. Determine if lines y = 2x + 5 and y = −0.5x − 3 are perpendicular.

5. Given a point (1,2), construct a line parallel to y = −3x + 7. That passing through this line.

6. Determine whether two points form a line perpendicular to (y = x).

7. Sketch two lines that are perpendicular and intersect at (0,0).

8. A design frame requires a beam to be perpendicular to a given reference line. Given the line (y = 2x − 4), construct the perpendicular beam passing through (3,1).

9. Two parts are aligned at angles given by (y = 5x + 2) and (y = −x + 7). Show if alignment is correct (i.e. perpendicular).

10. In a circuit board layout, two conductive paths must be parallel. One path follows the lane with equations of y = 0.75x + 5. Design another path through point (2,3).

🎬 Multimedia Task: Applications of Parallel and Perpendicular Lines

Duration: 1 Hour
Submission Format: Video or multimedia presentation
Tools Suggested: Any AI or digital content creation platform (e.g. Canva, Lumen5, Veed.io, CapCut, Adobe Express, etc.)

📝 Task Instructions:

You are required to work individually or in pairs to create a short video or multimedia presentation (1–3 minutes) that demonstrates real-world applications of parallel and perpendicular lines in your field of study (e.g. engineering, architecture, robotics, construction, automotive, etc.).

Your multimedia must include:

1. Definition and characteristics of parallel and perpendicular lines.

2. At least 1 real-world applications related to your diploma program for each lines.

3. Use of relevant images, icons, or videos.

4. A brief explanation (voiceover or text) describing how the applications involve parallel lines.

5. Creativity and clarity in delivery.

📊 Assessment Rubric (Total: 20 marks)

💡 Tips for Students:

• Keep your video short and focused (1–3 minutes).

• Use templates if needed for a fast and professional result.

• You may add subtitles or AI voiceovers if you're shy about recording your voice 😄.

• Cite or credit sources/images if taken from the web.

🎯 Quick Task: Watch & Identify Angle in Engineering

⏰ Duration: 5 minutes
📺 Watch: This short video

📝 Instructions:

1. Watch the video once or twice.

2. Look for where angles are used in the machines or actions shown.

3. In 1–2 sentences, write how angle is applied in the video (e.g. cutting, lifting, rotating, etc.).

4. Submit your answer to your lecturer or on the platform provided.

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Set 4 : Gradient and Angles Between Lines

Duration : 30 minutes

Answer the Following Exercise.

1. Find the gradient of a line passing through (1, 2) and (4, 5).

2. What is the gradient of a horizontal line?

3. Calculate angle between (y = 2x) and (y = −x).

4. Given slopes 3 and −1/3, find angle between lines.

5. Find gradient and angle between lines joining (2,3) to (5,7) and (5,7) to (8,3).

6. Interpret whether angle between two lines is acute, right or obtuse.

7. Two connecting rods form angles between their centre lines. If their slopes are 1 and 3, find the exact angle of intersection.

8. A structure requires a diagonal cross-brace forming a specific angle. Find the angle between (y = 2x) and (y = −3x + 5).

9. In bridge design, two beams meet with gradients of 1 and −1. Calculate the angle between them.

10. An inclined conveyor belt forms an angle of 20° with the horizontal. What is the gradient of the belt?

📝 Assignment Task: Literature Review on Coordinate Geometry Application

⏳ Duration: 1 Hour

📄 Submission Format: Short report / typed document (1–2 pages)

🧠 Objective:

To explore real-world problems that involve gradient and angle in Coordinate Geometry, and understand how these concepts are applied in engineering or technical fields.

🔍 Task Instructions:

You are required to:

1. Identify a real-world engineering or technical problem that involves gradient (slope) and/or angle from any online journal article, magazine, blog, or academic source.

2. Summarize the application of Coordinate Geometry in solving that problem.

3. Focus on how gradient and angle are used in analysis, design, construction, navigation, automation, or any relevant field.

4. Your write-up should include:

   • A brief problem description (1 paragraph)

   • An explanation of how gradient or angle is applied

   • Your reflection or opinion on its usefulness

   • Source citation (link or title of article/journal)

💡 Examples of Application Fields:

• Road / highway design (gradient of slopes)

• Robotic arm angle control

• Roof truss angle in construction

• Solar panel tilt optimization

• Drainage slope design

• Coordinate tracking in autonomous vehicles

📊 Assessment Rubric (Total: 20 marks)

🎯 Tips for Students:

• Search with keywords like "slope in construction", "application of gradient in engineering", or "angle in robotic design".

• Use trusted sources: Google Scholar, Engineering.com, ResearchGate, Medium, or reputable blogs.

• Keep your explanation short but meaningful — focus on how and why gradient/angle is used.

• Include diagrams or images if it helps you explain better (optional).