/20 1234567891011121314151617181920 Test Code: MC7L2 1 / 20 1. Find a relation between x and y if (x, y) is equidistant from (3, 6) and (–3, 4). A) x + y = 0 B) x² + y² = 9 C) 3x + y – 7 = 0 D) x – y = 1 Use distance formula: equate distances ⇒ get equation 3x + y – 7 = 0. 2 / 20 2. If the points A(2, 1), B(4, –1), and C(6, 1) form a triangle, find its type. A) Scalene B) Equilateral C) Isosceles D) Right-angled Using distance formula, AB = BC = √8 ⇒ Isosceles triangle. 3 / 20 3. What is the distance between green flag at (2, 25) and red flag at (8, 20)? A) 13 B) √125 C) √61 D) 10 Distance = √[(8 – 2)² + (20 – 25)²] = √[36 + 25] = √61. 4 / 20 4. Find the coordinates of a point dividing the line joining A(1, –2) and B(3, 6) in ratio 3:1 internally. A) (2.5, 4) B) (2, 2) C) (3, 2) D) (1, 1) x = (3×3 + 1×1)/(3+1) = 10/4 = 2.5, y = (3×6 + 1×–2)/4 = (18 – 2)/4 = 4. 5 / 20 5. If the area of triangle with vertices A(1, 2), B(4, y), and C(6, –3) is 15 sq units, find y. A) –3 or 7 B) 3 C) 2 D) 0 Apply area formula and solve: ±1/2 [1(y + 3) + 4(–3 – 2) + 6(2 – y)] = 15 ⇒ y = –3 or 7. 6 / 20 6. If point P lies on y-axis and is equidistant from A(2, 3) and B(–2, 3), what are its coordinates? A) (0, 3) B) (2, 0) C) (3, 2) D) (0, 2) Let P = (0, y). Use distance formula and symmetry about y-axis ⇒ y = 3. 7 / 20 7. Do the points (5, –2), (6, 4), and (7, –2) form an isosceles triangle? A) Equilateral B) Right angled C) No D) Yes Use distance formula. AB = BC ⇒ Two sides are equal ⇒ Isosceles. 8 / 20 8. What is the midpoint of the segment joining (2, –3) and (4, 1)? A) (3, 1) B) (3, –1) C) (2, 1) D) (2, –2) Midpoint formula: ((x1+x2)/2, (y1+y2)/2) = (6/2, –2/2) = (3, –1). 9 / 20 9. Find the value of k if A(2, 3), B(4, k), and C(6, –3) are collinear. A) 2 B) 0 C) 3 D) 1 Area of triangle = 0 ⇒ Use formula and solve for k: k = 0. 10 / 20 10. Are the points (1, 5), (2, 3), and (−2, −11) collinear? A) Always B) Can’t say C) Yes D) No Using distance formula, AB + BC ≠ AC ⇒ Points are not collinear. 11 / 20 11. Which of the following lies in the fourth quadrant? A) (–3, 5) B) (3, 5) C) (–3, –5) D) (3, –5) Fourth quadrant: x > 0 and y < 0 ⇒ (3, –5) satisfies this. 12 / 20 12. Find the coordinates of a point on the x-axis equidistant from (2, –5) and (–2, 9). A) (7, 0) B) (–7, 0) C) (2, 0) D) (0, 0) Let point be (x, 0). Use distance formula and solve equation for x. 13 / 20 13. If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find x. A) 3 B) 5 C) 0 D) 4 or –4 Use distance formula between QP and QR ⇒ solve equation for x. 14 / 20 14. What is the distance between the points (2, 3) and (4, 1)? A) 2 B) √10 C) 5 D) √8 Distance = √[(x2 – x1)² + (y2 – y1)²] = √[(4 – 2)² + (1 – 3)²] = √[4 + 4] = √8. 15 / 20 15. Find area of triangle formed by points (0, 0), (a, 0), (0, b). A) a – b B) a + b C) ab/2 D) ab Area = 1/2 × base × height = 1/2 × a × b = ab/2. 16 / 20 16. What is the length of diagonal of square with side 5 units? A) 10 B) 5√2 C) 5 D) 25 Diagonal = √(5² + 5²) = √50 = 5√2. 17 / 20 17. What is the area of triangle with vertices (2, 3), (4, 5), and (6, 1)? A) 10 B) 8 C) 5 D) 6 Use determinant formula: Area = 1/2 |x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)| = 6. 18 / 20 18. What values of y satisfy the condition: distance between P(2, –3) and Q(10, y) = 10? A) 10 B) 5, –11 C) 3 D) -2 Use distance formula: √[(10 – 2)² + (y + 3)²] = 10 ⇒ Solve the equation. 19 / 20 19. Find coordinates of point dividing (–1, 7) and (4, –3) in 2:3. A) (3, 2) B) (2, 1) C) (1, 3) D) (0, 0) Using section formula: x = (2×4 + 3×–1)/5 = 1, y = (2×–3 + 3×7)/5 = 3. 20 / 20 20. Find the distance between the origin and point (36, 15). A) 39 B) 21 C) 41 D) 51 Distance = √[(36 – 0)² + (15 – 0)²] = √(1296 + 225) = √1521 = 39.
