{
  "title": "Mid-point formula - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "📍 Midpoint of (2,3) and (4,5): 🎯", "options": {"A": "(3,4)", "B": "(4,3)", "C": "(2,4)", "D": "(3,3)"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "📐 Midpoint formula: x-coordinate = ? 🔢", "options": {"A": "(x₁+x₂)/2", "B": "(x₁-x₂)/2", "C": "x₁+x₂", "D": "x₁×x₂"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "🎯 Midpoint of (0,0) and (6,8): ⭐", "options": {"A": "(3,4)", "B": "(4,3)", "C": "(6,8)", "D": "(0,0)"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "📏 If midpoint is (5,6) and one endpoint is (2,3), other endpoint: ✏️", "options": {"A": "(8,9)", "B": "(7,8)", "C": "(6,7)", "D": "(4,5)"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "🔢 Midpoint divides segment in ratio: 🤔", "options": {"A": "1:1", "B": "2:1", "C": "1:2", "D": "3:1"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "📍 Midpoint of (-2,3) and (4,7): 🎨", "options": {"A": "(1,5)", "B": "(2,4)", "C": "(3,5)", "D": "(2,5)"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "📐 Midpoint y-coordinate formula: 🌈", "options": {"A": "(y₁+y₂)/2", "B": "(y₁-y₂)/2", "C": "y₁+y₂", "D": "y₁×y₂"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "🎯 Segment from (1,2) to (5,6). Midpoint? ⚡", "options": {"A": "(3,4)", "B": "(2,3)", "C": "(4,5)", "D": "(6,7)"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "📏 If endpoints are same, midpoint: 🔍", "options": {"A": "Same point", "B": "Different", "C": "Origin", "D": "Cannot find"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "🔢 Midpoint of (a,b) and (c,d): ✏️", "options": {"A": "((a+c)/2, (b+d)/2)", "B": "(a+c, b+d)", "C": "((a-c)/2, (b-d)/2)", "D": "(ac, bd)"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "📍 Midpoint lies on line joining: 🎯", "options": {"A": "Endpoints", "B": "Outside segment", "C": "Parallel line", "D": "Perpendicular"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "📐 If A(1,2), B(3,4), midpoint M. Distance AM = ? 📏", "options": {"A": "√2", "B": "√5", "C": "√8", "D": "√10"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "🎯 For horizontal segment, y-coordinate of midpoint equals: ⭐", "options": {"A": "Average of y's", "B": "0", "C": "1", "D": "x-coordinate"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "📏 Midpoint of (x₁,y₁) and (x₂,y₂) is origin if: 🔢", "options": {"A": "x₁=-x₂, y₁=-y₂", "B": "x₁=x₂, y₁=y₂", "C": "x₁=0, y₁=0", "D": "x₂=0, y₂=0"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "🔢 Triangle vertices (0,0), (4,0), (0,3). Midpoint of hypotenuse? 📐", "options": {"A": "(2,1.5)", "B": "(4,3)", "C": "(2,3)", "D": "(4,1.5)"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "📍 Quadrilateral vertices (0,0), (4,0), (4,3), (0,3). Midpoint of diagonal from (0,0) to (4,3)? 🎨", "options": {"A": "(2,1.5)", "B": "(4,1.5)", "C": "(2,3)", "D": "(4,3)"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "📐 If M is midpoint of AB, then AM = ? 🌈", "options": {"A": "MB", "B": "AB", "C": "2AB", "D": "AB/3"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "🎯 Midpoint coordinates are ______ of endpoints: ✏️", "options": {"A": "Average", "B": "Sum", "C": "Product", "D": "Difference"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "📏 Segment from (0,0) to (10,0). Midpoint? 🔍", "options": {"A": "(5,0)", "B": "(0,5)", "C": "(5,5)", "D": "(10,0)"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "🔢 Midpoint of (k,2k) and (3k,4k): ⚡", "options": {"A": "(2k,3k)", "B": "(k,3k)", "C": "(2k,2k)", "D": "(3k,2k)"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "📍 A(2,3), B(4,7). Find point dividing AB internally in ratio 1:1: 🎯", "options": {"A": "(3,5)", "B": "(2.5,4)", "C": "(3,4)", "D": "(4,5)"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "📐 Endpoints (x,3) and (5,y). Midpoint (3,5). Find x,y: 🔢", "options": {"A": "x=1, y=7", "B": "x=2, y=6", "C": "x=4, y=8", "D": "x=6, y=4"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "🎯 Triangle vertices (1,2), (3,4), (5,6). Midpoints of sides form: ⭐", "options": {"A": "Triangle", "B": "Parallelogram", "C": "Line", "D": "Point"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "📏 A(1,1), B(5,3), C(3,5). Midpoints of AB, BC, CA form triangle. Its area? 📊", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "🔢 Quadrilateral vertices (0,0), (a,0), (a,b), (0,b). Midpoints form: 🎨", "options": {"A": "Parallelogram", "B": "Rectangle", "C": "Rhombus", "D": "Square"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "📍 Line segment from (1,2) to (5,6) divided into 4 equal parts. Second division point? ✏️", "options": {"A": "(3,4)", "B": "(2,3)", "C": "(4,5)", "D": "(2.5,3.5)"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "📐 Midpoint of hypotenuse of right triangle (0,0), (6,0), (0,8) is: 🔍", "options": {"A": "(3,4)", "B": "(4,3)", "C": "(6,8)", "D": "(0,0)"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "🎯 A(2,3), midpoint M(4,5). Find B: ⚡", "options": {"A": "(6,7)", "B": "(5,6)", "C": "(3,4)", "D": "(8,10)"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "📏 Three points A(1,2), B(3,4), C(5,6) are collinear. Midpoint of AC? 🌈", "options": {"A": "(3,4)", "B": "(2,3)", "C": "(4,5)", "D": "(6,7)"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "🔢 Rectangle vertices (0,0), (8,0), (8,6), (0,6). Midpoint of diagonal from (0,0) to (8,6)? 📐", "options": {"A": "(4,3)", "B": "(8,3)", "C": "(4,6)", "D": "(8,6)"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "📍 Line joining midpoints of two sides of triangle is ______ to third side: 🎯", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Equal", "D": "Twice"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "📐 A(1,2), B(3,4), C(5,8). Midpoint of AB is M, of BC is N. Length MN? 📏", "options": {"A": "√5", "B": "√10", "C": "√13", "D": "√17"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "🎯 Points A(2,3), B(4,5), C(6,7) are collinear. Ratio in which B divides AC? ⭐", "options": {"A": "1:1", "B": "1:2", "C": "2:1", "D": "3:1"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "📏 Segment from (x₁,y₁) to (x₂,y₂) is divided by midpoint. Coordinates of quarter point from first end? ✏️", "options": {"A": "((3x₁+x₂)/4, (3y₁+y₂)/4)", "B": "((x₁+x₂)/4, (y₁+y₂)/4)", "C": "((x₁+3x₂)/4, (y₁+3y₂)/4)", "D": "((x₁-x₂)/4, (y₁-y₂)/4)"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "🔢 Triangle ABC, A(0,0), B(6,0), C(0,8). Midpoint of BC is D. Length AD? 📐", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "📍 Points A(1,3), B(2,5), C(4,9). Which point is midpoint of other two? 🎨", "options": {"A": "B is midpoint of AC", "B": "C is midpoint of AB", "C": "A is midpoint of BC", "D": "None"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "📐 Quadrilateral midpoints joined form parallelogram. This is ______ theorem: 🔍", "options": {"A": "Varignon's", "B": "Pythagoras", "C": "Thales", "D": "Apollonius"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "🎯 A(2,4), midpoint M(3,5). If B is other end, and C is midpoint of AM, find C: ⚡", "options": {"A": "(2.5,4.5)", "B": "(3,5)", "C": "(4,6)", "D": "(5,7)"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "📏 Line segment from (a,b) to (c,d) has midpoint at origin. Then: 🌈", "options": {"A": "a=-c, b=-d", "B": "a=c, b=d", "C": "a=0, b=0", "D": "c=0, d=0"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "🔢 Points (2,3), (4,5), (6,7) have same midpoint when paired differently? 🤔", "options": {"A": "No", "B": "Yes", "C": "Sometimes", "D": "Always"}, "correct_answer": "A"},
    
    {"id": 41, "difficulty": "hard", "question": "📍 Triangle vertices A(0,0), B(6,0), C(0,8). Find coordinates of centroid using midpoints: 🎯", "options": {"A": "(2, 8/3)", "B": "(3,4)", "C": "(4,3)", "D": "(6,8)"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "📐 Points A(1,2), B(3,4), C(5,6), D(7,8) form parallelogram. Find intersection of diagonals: 🔢", "options": {"A": "(4,5)", "B": "(3,4)", "C": "(5,6)", "D": "(6,7)"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "🎯 Line joining midpoints of diagonals of trapezium is parallel to bases. Length if bases are 10 and 6? 📏", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "📏 Vertices of triangle are (0,0), (x₁,y₁), (x₂,y₂). Midpoints of sides form triangle with vertices: ✏️", "options": {"A": "((x₁)/2, y₁/2), ((x₂)/2, y₂/2), ((x₁+x₂)/2, (y₁+y₂)/2)", "B": "same as original", "C": "twice original", "D": "half coordinates"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "🔢 Points A(2,3), B(4,7), C(6,11) are collinear. Find point dividing AC in ratio equal to AB:BC: 🎨", "options": {"A": "((2+6)/2, (3+11)/2)", "B": "((4+6)/2, (7+11)/2)", "C": "((2+4)/2, (3+7)/2)", "D": "((4+8)/2, (7+15)/2)"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "📍 Median of triangle joins vertex to midpoint of opposite side. Triangle (0,0), (6,0), (0,8). Length of median from (0,0)? 📐", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "📐 Four points (0,0), (a,0), (a,b), (0,b). Line joining midpoints of opposite sides intersect at: 🔍", "options": {"A": "(a/2, b/2)", "B": "(a,b)", "C": "(0,0)", "D": "(a/4, b/4)"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "🎯 A(1,2), B(3,4). Point P on AB such that AP:PB = m:n. If P is midpoint, then: ⭐", "options": {"A": "m=n", "B": "m=2n", "C": "n=2m", "D": "m=3n"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "📏 Triangle vertices (x₁,y₁), (x₂,y₂), (x₃,y₃). Midpoint of side joining first two is M. Distance from M to third vertex? ✏️", "options": {"A": "½√[(x₃-(x₁+x₂)/2)² + (y₃-(y₁+y₂)/2)²]", "B": "√[(x₃-x₁)²+(y₃-y₁)²]", "C": "√[(x₃-x₂)²+(y₃-y₂)²]", "D": "½√[(x₃-x₁)²+(y₃-y₁)²]"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "🔢 Points A(1,3), B(2,5), C(4,9), D(5,11). Show ABCD is parallelogram using midpoints: 🎯", "options": {"A": "Midpoints of AC and BD coincide", "B": "Midpoints of AB and CD coincide", "C": "Midpoints of AD and BC coincide", "D": "All midpoints same"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "📍 Line segment from (0,0) to (10,0) divided into n equal parts. Midpoint of k-th segment? 📏", "options": {"A": "((2k-1)×10/(2n), 0)", "B": "(k×10/n, 0)", "C": "((k-1)×10/n, 0)", "D": "(k×10/(2n), 0)"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "📐 Triangle ABC, A(0,0), B(6,0), C(3,4). Midpoints of sides form triangle. Ratio of areas (new:original)? 📊", "options": {"A": "1:4", "B": "1:2", "C": "1:3", "D": "2:3"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "🎯 Points A(1,1), B(5,3), C(3,7). Midpoints of AB, BC, CA form triangle. Its centroid? ⚡", "options": {"A": "(3, 11/3)", "B": "(3,4)", "C": "(4,3)", "D": "(11/3, 3)"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "📏 Segment AB, A(2,3), B(6,7). Find point P such that AP:PB = 3:1 using midpoint concept: 🌈", "options": {"A": "First find midpoint of AB, then midpoint of MB where M is midpoint", "B": "Direct formula", "C": "Cannot find", "D": "P is midpoint of AB"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "🔢 Three points A(1,2), B(3,6), C(5,10). If M is midpoint of AB, N of BC, then MN is parallel to: 📐", "options": {"A": "AC", "B": "AB", "C": "BC", "D": "None"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "📍 Four points (0,0), (4,0), (4,3), (0,3). Line joining midpoints of sides forms: 🎨", "options": {"A": "Rhombus", "B": "Rectangle", "C": "Square", "D": "Parallelogram"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "📐 Points A(2,4), B(4,8), C(6,12). Midpoint of AC is M. Point dividing MB in ratio 2:1 is? 🔍", "options": {"A": "(14/3, 28/3)", "B": "(5,10)", "C": "(16/3, 32/3)", "D": "(6,12)"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "🎯 Triangle vertices (0,0), (a,0), (0,b). Midpoints of sides form triangle. Its area? 📊", "options": {"A": "ab/8", "B": "ab/4", "C": "ab/2", "D": "ab"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "📏 Segment from (x₁,y₁) to (x₂,y₂). Point dividing in ratio m:n has coordinates using weighted average. If m=n, we get: ✏️", "options": {"A": "Midpoint", "B": "Endpoint", "C": "Quarter point", "D": "Three-quarter point"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "🔢 A(1,2), B(3,4), C(5,6). D is midpoint of AB, E of BC, F of CA. Area of triangle DEF? 📐", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"}
  ]
}