Question 31 - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Nov. 1, 2019 by Teachoo

Two friends Seema and Aditya work in the same office at Delhi. In the Christmas vacations, both decided to go to their hometowns represented by Town A and Town B respectively in the figure given below. Town A and Town B are connected by trains from the same station C (in the given figure)in Delhi. Based on the given situation, answer the following questions:

(i) Who will travel more distance, Seema or Aditya, to reach to their hometown?

(ii) Seema and Aditya planned to meet at a location D situated at a point D represented by the mid-point of the line joining the points represented by Town A and Town B. Find the coordinates of the point represented by the point D

(iii) Find the area of the triangle formed by joining the points represented by A, B and C.

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Question 31 Two friends Seema and Aditya work in the same office at Delhi. In the Christmas vacations, both decided to go to their hometowns represented by Town A and Town B respectively in the figure given below. Town A and Town B are connected by trains from the same station C (in the given figure)in Delhi. Based on the given situation, answer the following questions:
Plotting points in the graph
(i) Who will travel more distance, Seema or Aditya, to reach to their hometown?
Now,
We need to find distance AC and AB
Distance AC
Point A (1, 7) and C (β4, 4)
AC = β((π₯_2βπ₯_1 )^2+(π¦_2βπ¦_1 )^2 )
= β((β4β1)^2+(4β7)^2 )
= β((β5)^2+(β3)^2 )
= β(5^2+3^2 )
= β(25+9)
= β34
Distance BC
Point B (4, 2) and C (β4, 4)
BC = β((π₯_2βπ₯_1 )^2+(π¦_2βπ¦_1 )^2 )
= β((β4β4)^2+(4β2)^2 )
= β((β8)^2+(2)^2 )
= β(8^2+2^2 )
= β(64+4)
= β68
Since BC > AC
So, Aditya travels more distance
(ii) Seema and Aditya planned to meet at a location D situated at a point D represented by the mid-point of the line joining the points represented by Town A and Town B. Find the coordinates of the point represented by the point D
We need to find mid-point of AB
Mid point of A(1, 7) & B(4, 2)
= ((π₯_1 + π₯_2)/2, (π¦_1 + π¦_2)/2) = ((1 + 4)/2, (7 + 2)/2) = (π/π, π/π)
(iii) Find the area of the triangle formed by joining the points represented by A, B and C.
Coordinates of Point A (1, 7), B (4, 2) and C (β4, 4)
Area of triangle ABC = 1/2 [ x1(y2 β y3) + x2(y3 β y1) + x3(y1 β y2) ]
Here
x1 = 1 , y1 = 7
x2 = 4 , y2 = 2
x3 = β4 , y3 = 4
Putting values
Area of triangle ABC = 1/2 [ 1(2 β 4) + 4(4 β 7) + (β4)(7 β 2)]
= 1/2 [ 1 Γ (β2) + 4 Γ (β3) + (β4) Γ 5]
= 1/2 [ β2 β 12 β 20]
= 1/2 [ β34]
= β17
Hence, Area of Ξ ABC is 17 square units

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.