CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Question 17 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Last updated at Oct. 27, 2020 by Teachoo

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

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

CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.