Question 17 (Case Based Question) - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

Case Study based - SUN ROOM

The diagrams show the plans for a sun room. It will be built onto the wall of a house. The four walls of the sunroom are square clear glass panels. The roof is made using

Four clear glass panels, trapezium in shape, all the same size

One tinted glass panel, half a regular octagon in shape

Question 17 Case Study Based-1 SUN ROOM The diagrams show the plans for a sun room. It will be built onto the wall of a house. The four walls of the sunroom are square clear glass panels. The roof is made using • Four clear glass panels, trapezium in shape, all the same size • One tinted glass panel, half a regular octagon in shape(a) Refer to Top View Find the mid-point of segment joining the points J (6, 17) & I (9, 16). (i) (33/2,15/2) (ii) (3/2,1/2) (iii) (15/2,33/2) (iv) (1/2,3/2)
Mid point of line segment joining J (6, 17) & I (9, 16) is
Mid point = ((6 + 9)/2 ,(17 + 16)/2 )
= (𝟏𝟓/𝟐 ,𝟑𝟑/𝟐 )
So, (iii) is correct
(b) Refer to Top View The distance of the point P from the y-axis is (i) 4 (ii) 15 (iii) 19 (iv) 25
Distance of Point P from y-axis is 4
(c) Refer to Front View The distance between the points A and S is (i) 4 (ii) 8 (iii) 16 (iv) 20
Distance between the points A and S is 16
(d) Refer to Front View Find the co-ordinates of the point which divides the line segment joining the points A and B in the ratio 1:3 internally. (i) (8.5,2.0) (ii) (2.0,9.5) (iii) (3.0,7.5) (iv) (2.0,8.5)Here,
Here,
Point A(1, 8) and B (5, 11)
Let Point X (x, y) divide AB in ratio 1:3 internally
Therefore,
Coordinates of X = ((1(5) + 3(1))/(1 + 3),(1(10) + 3(8))/(1 + 3))
= ((5 + 3)/4,(10 + 24)/4)
= (8/4,34/4)
= (2, 8.5)
(e) Refer to Front View If a point (x, y) is equidistant from the Q(9, 8) and S(17, 8), then (i) x + y = 13 (ii) x – 13 = 0 (iii) y – 13 = 0 (iv )x – y = 13
Let required point be X (x, y)
Now, Point X is equidistant from Q(9, 8) & S (17, 8)
Hence,
QX = SX
√((𝑥 −9)2+(𝑦−8)2) = √((𝑥 −17)2+(𝑦−8)2)
Squaring both sides
(𝑥 −9)2+(𝑦−8)2=(𝑥 −17)2+(𝑦−8)2
(𝑥 −9)2=(𝑥 −17)2
𝑥^2+9^2−18𝑥=𝑥^2+17^2−34𝑥
34𝑥−18𝑥=17^2−9^2
16𝑥=(17−9)(17+9)
16𝑥=8 × 26
𝑥=(8 × 26)/16
𝑥=13
𝒙−𝟏𝟑=𝟎
So, (ii) is correct

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!