{
  "title": "Section Formula - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Midpoint of (2, 3) and (4, 5) is? 📍", "options": {"A": "(3, 4)", "B": "(2, 4)", "C": "(3, 5)", "D": "(4, 3)"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Midpoint of (0, 0) and (6, 8) is? 🎯", "options": {"A": "(3, 4)", "B": "(6, 8)", "C": "(0, 0)", "D": "(4, 3)"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Midpoint of (-1, 2) and (3, 4) is? 📐", "options": {"A": "(1, 3)", "B": "(2, 3)", "C": "(1, 2)", "D": "(2, 2)"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Midpoint of (5, 7) and (9, 11) is? ✨", "options": {"A": "(7, 9)", "B": "(5, 9)", "C": "(7, 11)", "D": "(9, 7)"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Midpoint of (2, 2) and (8, 8) is? 🔢", "options": {"A": "(5, 5)", "B": "(4, 4)", "C": "(6, 6)", "D": "(3, 3)"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Midpoint of (-3, -4) and (5, 6) is? 📏", "options": {"A": "(1, 1)", "B": "(2, 2)", "C": "(4, 5)", "D": "(-1, -1)"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Midpoint of (10, 20) and (30, 40) is? 🧮", "options": {"A": "(20, 30)", "B": "(15, 25)", "C": "(25, 35)", "D": "(30, 20)"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Midpoint of (a, b) and (c, d) is? 📐", "options": {"A": "((a+c)/2, (b+d)/2)", "B": "(a+c, b+d)", "C": "((a-c)/2, (b-d)/2)", "D": "(a/2, b/2)"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "If midpoint of (x, 3) and (5, y) is (3, 4), then x=? y=? 🤔", "options": {"A": "x=1, y=5", "B": "x=5, y=3", "C": "x=2, y=6", "D": "x=4, y=2"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Midpoint of (0, 5) and (10, 15) is? 📍", "options": {"A": "(5, 10)", "B": "(0, 10)", "C": "(5, 15)", "D": "(10, 10)"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Midpoint of (-2, -2) and (2, 2) is? 🎯", "options": {"A": "(0, 0)", "B": "(1, 1)", "C": "(-1, -1)", "D": "(2, 2)"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Midpoint of (3, 0) and (7, 0) is? 📏", "options": {"A": "(5, 0)", "B": "(3, 0)", "C": "(0, 5)", "D": "(7, 0)"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Midpoint of (0, 4) and (0, 10) is? 📐", "options": {"A": "(0, 7)", "B": "(4, 10)", "C": "(7, 0)", "D": "(0, 5)"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "If midpoint is (4, 6) and one end is (2, 4), other end? 🔄", "options": {"A": "(6, 8)", "B": "(8, 10)", "C": "(4, 8)", "D": "(6, 10)"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Midpoint of (1, 2) and (1, 8) is? 📍", "options": {"A": "(1, 5)", "B": "(2, 5)", "C": "(1, 10)", "D": "(0, 5)"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Midpoint of (6, 9) and (6, 3) is? 🎯", "options": {"A": "(6, 6)", "B": "(9, 6)", "C": "(3, 6)", "D": "(6, 12)"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Midpoint of (-5, 7) and (5, 7) is? 📏", "options": {"A": "(0, 7)", "B": "(5, 7)", "C": "(-5, 7)", "D": "(0, 0)"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Midpoint of (8, -3) and (8, 5) is? 📐", "options": {"A": "(8, 1)", "B": "(8, -1)", "C": "(0, 1)", "D": "(8, 0)"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Midpoint of (x₁, y₁) and (x₂, y₂) formula? 🧮", "options": {"A": "((x₁+x₂)/2, (y₁+y₂)/2)", "B": "(x₁+x₂, y₁+y₂)", "C": "((x₁-x₂)/2, (y₁-y₂)/2)", "D": "(x₁/2, y₁/2)"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "If A(1,2), B(3,4), midpoint M coordinates? 📍", "options": {"A": "(2, 3)", "B": "(1, 3)", "C": "(2, 4)", "D": "(3, 2)"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Point dividing (1, 2) and (4, 5) in ratio 1:2 is? 🔢", "options": {"A": "(2, 3)", "B": "(3, 4)", "C": "(1, 2)", "D": "(4, 5)"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Point dividing (0, 0) and (6, 9) in ratio 2:1 is? 📐", "options": {"A": "(4, 6)", "B": "(2, 3)", "C": "(3, 4.5)", "D": "(6, 9)"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Point dividing (2, 3) and (5, 6) in ratio 1:1 is? 📍", "options": {"A": "(3.5, 4.5)", "B": "(2, 3)", "C": "(5, 6)", "D": "(3, 4)"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Point dividing (4, 5) and (10, 11) in ratio 3:1 is? 🎯", "options": {"A": "(8.5, 9.5)", "B": "(7, 8)", "C": "(5.5, 6.5)", "D": "(9, 10)"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Point dividing (-1, -2) and (5, 10) in ratio 1:2 is? 📏", "options": {"A": "(1, 2)", "B": "(2, 4)", "C": "(3, 6)", "D": "(0, 0)"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "If P divides A(1,2) and B(4,8) in ratio 2:1, P = ? 🤔", "options": {"A": "(3, 6)", "B": "(2, 4)", "C": "(4, 8)", "D": "(1, 2)"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Point dividing (3, 7) and (9, 13) in ratio 1:2 is? 📐", "options": {"A": "(5, 9)", "B": "(7, 11)", "C": "(4, 8)", "D": "(6, 10)"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "If A(0,0), B(12,0), point dividing in 3:1 ratio? 📍", "options": {"A": "(9, 0)", "B": "(3, 0)", "C": "(6, 0)", "D": "(4, 0)"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "If A(0,0), B(0,8), point dividing in 1:3 ratio? 🎯", "options": {"A": "(0, 2)", "B": "(0, 4)", "C": "(0, 6)", "D": "(0, 1)"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Section formula for point dividing (x₁,y₁) and (x₂,y₂) in m:n? 🧮", "options": {"A": "((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))", "B": "((mx₁+nx₂)/(m+n), (my₁+ny₂)/(m+n))", "C": "((x₁+x₂)/2, (y₁+y₂)/2)", "D": "(x₁+ x₂, y₁+ y₂)"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "If point P divides A(2,3) and B(5,7) in ratio k:1 and P is (4,5), find k. 🔢", "options": {"A": "2", "B": "1", "C": "3", "D": "0.5"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Point dividing join of (-2, 3) and (4, 9) in ratio 2:1 is? 📏", "options": {"A": "(2, 7)", "B": "(0, 5)", "C": "(1, 6)", "D": "(3, 8)"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Point dividing (1, 4) and (7, 10) in ratio 1:1 is? 📐", "options": {"A": "(4, 7)", "B": "(3, 6)", "C": "(5, 8)", "D": "(2, 5)"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If midpoint of (a, 5) and (3, b) is (2, 6), find a,b. 🤔", "options": {"A": "a=1, b=7", "B": "a=4, b=5", "C": "a=3, b=6", "D": "a=2, b=7"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Point dividing (0,0) and (8,12) in ratio 3:5 is? 📍", "options": {"A": "(3, 4.5)", "B": "(5, 7.5)", "C": "(2, 3)", "D": "(6, 9)"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Point dividing (5, 5) and (20, 20) in ratio 1:4 is? 🎯", "options": {"A": "(8, 8)", "B": "(10, 10)", "C": "(12, 12)", "D": "(15, 15)"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "If A(1,1), B(4,4), point dividing AB in 2:3 ratio? 📏", "options": {"A": "(2.2, 2.2)", "B": "(2.5, 2.5)", "C": "(3, 3)", "D": "(2, 2)"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Point dividing (10, 2) and (2, 10) in ratio 1:1 is? 📐", "options": {"A": "(6, 6)", "B": "(8, 8)", "C": "(4, 4)", "D": "(5, 5)"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If P(2,3) is midpoint of A(a,5) and B(4,b), find a,b. 🤔", "options": {"A": "a=0, b=1", "B": "a=1, b=2", "C": "a=3, b=4", "D": "a=2, b=3"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Point dividing (3, -2) and (-7, 4) in ratio 2:3 is? 📍", "options": {"A": "(-1, 0.4)", "B": "(-2, 1)", "C": "(0, 0)", "D": "(1, -0.4)"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "Point dividing (4, 5) and (7, 11) externally in ratio 2:1 is? 🔄", "options": {"A": "(10, 17)", "B": "(5.5, 8.5)", "C": "(6, 9)", "D": "(8, 13)"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "If A(1,2), B(4,5), point dividing AB externally in ratio 3:2 is? 📐", "options": {"A": "(10, 11)", "B": "(7, 8)", "C": "(5.5, 6.5)", "D": "(8, 9)"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "Coordinates of centroid of triangle with vertices (0,0), (6,0), (0,8)? 📍", "options": {"A": "(2, 8/3)", "B": "(6, 8)", "C": "(3, 4)", "D": "(2, 2)"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "Centroid of triangle (1,2), (3,4), (5,6) is? 🎯", "options": {"A": "(3, 4)", "B": "(2, 3)", "C": "(4, 5)", "D": "(1, 2)"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "If centroid of triangle (x,3), (5,y), (2,4) is (3,4), find x,y. 🤔", "options": {"A": "x=2, y=5", "B": "x=4, y=3", "C": "x=3, y=4", "D": "x=1, y=6"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Point dividing line joining (1,-2) and (-3,4) in ratio 1:2 internally? 📏", "options": {"A": "(-1/3, 0)", "B": "(0, 0)", "C": "(-1, 2)", "D": "(1, -2)"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "If point (3,4) divides (5,7) and (x,y) in ratio 2:3, find (x,y). 🔢", "options": {"A": "(0, 1)", "B": "(1, 2)", "C": "(2, 3)", "D": "(4, 5)"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "Point dividing (a,b) and (c,d) in ratio m:n externally formula? 🧮", "options": {"A": "((mx₂ - nx₁)/(m-n), (my₂ - ny₁)/(m-n))", "B": "((mx₁ - nx₂)/(m-n), (my₁ - ny₂)/(m-n))", "C": "((x₁+x₂)/2, (y₁+y₂)/2)", "D": "same as internal"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "If A(2,3), B(4,5) and P divides AB such that AP:PB = 3:2, find P. 📍", "options": {"A": "(3.2, 4.2)", "B": "(3, 4)", "C": "(2.8, 3.8)", "D": "(3.5, 4.5)"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "If P(1,2), Q(4,5) and R divides PQ externally in ratio 5:2, R = ? 🎯", "options": {"A": "(9, 12)", "B": "(6, 9)", "C": "(11, 14)", "D": "(8, 11)"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "The points (1,2), (4,y), (x,6), (3,5) are vertices of a parallelogram taken in order. Find x,y. 🔳", "options": {"A": "x=6, y=3", "B": "x=5, y=4", "C": "x=4, y=5", "D": "x=3, y=6"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "Find ratio in which point (2,3) divides (1,2) and (4,5). 📐", "options": {"A": "1:2", "B": "2:1", "C": "1:1", "D": "3:1"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "Find ratio in which y-axis divides (-3,5) and (2,-5). 📏", "options": {"A": "3:2", "B": "2:3", "C": "1:1", "D": "5:2"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "If point (a,b) divides (1,2) and (5,6) in ratio 1:3, find a+b. 🔢", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "If centroid of triangle is (2,3) and two vertices are (1,2) and (3,4), third vertex? 📍", "options": {"A": "(2, 3)", "B": "(4, 5)", "C": "(0, 1)", "D": "(2, 5)"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Point dividing (2,3) and (5,7) in ratio equal to ratio of their distances from origin? 🎯", "options": {"A": "(3.5, 5.2)", "B": "(3, 4)", "C": "(4, 6)", "D": "(2.8, 4.2)"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "If A(-1,2), B(3,4), find point on AB extended such that AB:BP = 3:2. 📏", "options": {"A": "(7, 6)", "B": "(5, 5)", "C": "(6, 5.5)", "D": "(8, 7)"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Points A(2,3), B(4,5), C(6,7) are collinear. Find ratio AB:BC. 📐", "options": {"A": "1:1", "B": "2:1", "C": "1:2", "D": "3:1"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "If (x,y) is midpoint of (1,2) and (5,8), then (x+1, y+1) divides (1,2) and (5,8) in ratio? 🤔", "options": {"A": "3:1", "B": "2:1", "C": "1:1", "D": "1:2"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Point dividing line joining origin and (10,15) in ratio equal to golden ratio (1.618:1) approximately? 🌟", "options": {"A": "(6.18, 9.27)", "B": "(5, 7.5)", "C": "(7, 10.5)", "D": "(8, 12)"}, "correct_answer": "A"}
  ]
}