Question 3 - Case Based Questions (MCQ) - Chapter 7 Class 10 Coordinate Geometry

Transcript

Question Ayush Starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter's school and then reaches the office. (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km. Question 1 What is the distance between house and bank? (a) 5 km (b) 10 km (c) 12 km (d) 27 km Given that House (2, 4) & Bank (5, 8) Now, Distance b/w house and bank = √((𝑥_2−𝑥_1 )^2+(𝑦_2−𝑦_1 )^2 ) = √((𝟓−𝟐)^𝟐+(𝟖−𝟒)^𝟐 ) = √((3)^2+(4)^2 ) = √(9+16) = √25 = √(5^2 ) = 5 km So, the correct answer is (B) Question 2 What is the distance between Daughter's School and bank? (a) 5 km (b) 10 km (c) 12 km (d) 27 km Given that School (13, 14) & Bank (5, 8) Now, Distance b/w school and bank = √((𝑥_2−𝑥_1 )^2+(𝑦_2−𝑦_1 )^2 ) = √((𝟓−𝟏𝟑)^𝟐+(𝟖−𝟏𝟒)^𝟐 ) = √((−8)^2+(−6)^2 ) = √(64+36) = √100 = √(10^2 ) = 10 km So, the correct answer is (B) Question 3 What is the distance between house and office? (a) 24.6 km (b) 26.4 km (c) 24 km (d) 26 km Given that House (2, 4) & Office (13, 26) Now, Distance b/w house and office = √((𝑥_2−𝑥_1 )^2+(𝑦_2−𝑦_1 )^2 ) = √((𝟏𝟑−𝟐)^𝟐+(𝟐𝟔−𝟒)^𝟐 ) = √((11)^2+(22)^2 ) = √((11)^2+(2 × 11)^2 ) = √((11)^2+2^2 (11)^2 ) = √((11)^2 (1+2^2 ) ) = √((11)^2 (1+4) ) = √((11)^2 × 5) = 𝟏𝟏√𝟓 = 11 × 2.23 = 24.53 km ~ 24.6 km So, the correct answer is (A) Question 4 What is the total distance travelled by Ayush to reach the office? (a) 5 km (b) 10 km (c) 12 km (d) 27 km Now, our diagram looks like Let’s find Distance from School to Office Given that House (13, 14) & Office (13, 26) Now, Distance b/w school and office = √((𝑥_2−𝑥_1 )^2+(𝑦_2−𝑦_1 )^2 ) = √((𝟏𝟑−𝟏𝟑)^𝟐+(𝟐𝟔−𝟏𝟒)^𝟐 ) = √(0^2+(12)^2 ) = √(12^2 ) = 12 km Thus, our diagram looks like Total distance travelled = House to Bank + Bank to School + School to Office = 5 + 10 + 12 = 27 km So, the correct answer is (D) Question 5 What is the extra distance travelled by Ayush? (a) 2 km (b) 2.2 km (c) 2.4 km (d) none of these Extra distance travelled by Ayush = Distance travelled − Distance from House to Office = 27 – 24.6 = 2.4 km So, the correct answer is (C)