Question 4 - Case Based Questions (MCQ) - Chapter 7 Class 10 Coordinate Geometry

Transcript

Question In a room, 4 friends are seated at the points A, B, C and D as shown in figure. Reeta and Meeta walk into the room and after observing for a few minutes, Reeta asks Meeta Let’s find coordinates of points A, B, C, D Thus, coordinates of the 4 points are A(3, 4), B(6, 7), C(9, 4) , D(6, 1) Question 1 What is the position of A? (a) (4, 3) (b) (3, 3) (c) (3, 4) (d) None of these From figure Position of A = (3, 4) So, the correct answer is (a) Question 2 What is the middle position of B and C? (a) (15/2,11/2) (b) (2/15,11/2) (c) (1/2,1/2) (d) None of these We need to find Mid-point of B (6, 7) and C (9, 4) Now, Coordinates of mid-point = ((𝑥_1 + 𝑥_2)/2,(𝑦_1 + 𝑦_2)/2) = ((6 + 9)/2,(7 + 4)/2) = (𝟏𝟓/𝟐,𝟏𝟏/𝟐) So, the correct answer is (a) Question 3 What is the position of D? (a) (6, 0) (b) (0, 6) (c) (6, 1) (d) (1, 6) From figure Position of D = (6, 1) So, the correct answer is (a) Question 4 What is the distance between A and B? (a) 3√2 unit (b) 2√3 unit (c) 2√2 unit (d) 3√3 unit Finding AB AB = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −3)2+(7 −4)2) = √((3)2+(3)2) = √(2(3)2) = 3√𝟐 units So, the correct answer is (a) Question 5 What is the distance between C and D? (a) √2 unit (b) 2√2 unit (c) 3√2 unit (d) 4√2 unit Finding CD CD = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 9 −6)2+(4 −1)2) = √((3)2+(3)2) = √(2(3)2) = 3√𝟐 units So, the correct answer is (c)