RD Chapter 7 Introduction to Euclid s Geometry Ex 7.3 Solutions
Question - 11 : - A number is 27 more than the number obtained by reversing its digits. If its unit’s and ten’s digit are x and y respectively, write the linear equation representing the above statement.
Answer - 11 : -
Let unit’s digit = x
and tens digit = y
∴ Number = x + 10y
By reversing the digits, units digit = y
and ten’s digit = x
∴ number = y + 10x
Now difference of these two numbers = 27 (x + 10y) – (y +10x) = 27
x + 10y – y – 10x = 27
⇒ -9x + 9y – 27 = 0
⇒ x-_y + 3 = 0 (Dividing by -9)
Hence equation is x – y + 3 = 0
Question - 12 : - The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten’s digit of the number are x and y respectively, then write the linear equation representing the above statement.
Answer - 12 : -
Let unit digit = x
and tens digit = y
∴ Number = x + 10y
By reversing the digits,
units digit = y
and tens digit = x
∴ Number =y+ 10x
Now sum of these two numbers = 121
∴ x + 10y + y + 10x = 121
⇒ 1 lx + 11y = 121
⇒ x + y = 11 (Dividing by 11)
∴ x + y = 11
Question - 13 : - Draw the graph of the equation 2x + y = 6. Shade the region bounded by the graph and the coordinate axes. Also find the area of the shaded region.
Answer - 13 : -
2x + y = 6
⇒ y = 6 – 2x
If x = 0, then y = 6- 2 x 0 = 6 – 0 = 6
If x = 2, then y = 6- 2 x 2 = 6- 4 = 2
Now plot the points (0, 6) and (2, 2) on the graph and join them to get a line which intersects x-axis at (3, 0) and y-axis at (0,6)
Now co-ordinates if vertices of the shaded portion are (6, 0) (0, 0) and (3, 0) Now area of the shaded region.
Question - 14 : - Draw the graph of the equation 
Also find the area of the triangle formed by the line and the co-ordinate axes.
Answer - 14 : -
Now plot the points (3, 0) and (0, 4) and join them to get a line which interest x-axis at A (3, 0) and y-axis at B (0, 4)
Question - 15 : - Draw the graph of y = | x |
Answer - 15 : - y = | x |
⇒ y = x [∵ | x |=x]
∴ Now taking z points.
Now plot the points (1, 1) (2, 2) and (3, 3) and join them to get a graph of a line.
Question - 16 : - Draw the graph of y = | x | + 2
Answer - 16 : -
y – | x | + 2
⇒ y = x + 2 [| x | = x]
If x = 0, then y = 0 + 2 = 2
If x = 1, then y = 1+2 = 3
If x = 2, then y = 2 + 2 = 4
Now plot the points (0, 2), (1, 3) and (2, 4) on the graph and join them to get a line.
Question - 17 : - Draw the graphs of the following linear equation on the same graph paper.
2x + 3y = 12, x -y = 1
Find the co-ordinates of the vertices of the triangle formed by the two straight lines and the y-axis. Also find the area of the triangle.
Answer - 17 : -
Now plot the points (6, 0) (0, 4) on the graph to get a line.
Now plot the points (1, 0) and (2, 1) on the graph to get another line.
Area of the triangle FEB so formed,
= 
FB x FL = x 5 x 3 = 15/2
= 7.5 sq. units
co-ordinates of E, F, B are E (3, 2), (0, -1) and (0, 4)
Question - 18 : - Draw the graphs of the linear equations 4x – 3y + 4 = 0 and 4x + 3y – 20 = 0. Find the area bounded by these lines and x-axis.
Answer - 18 : -
Now plot the points (5, 0) and (2, 4)and join them to get a line we see that the ΔABC is formed by bounding there line with x-axis.
Question - 19 : - The path of a train A is given by the equation 3x + 4y – 12 = 0 and the path of another train B is given by the equation 6jc + 8y – 48 = 0. Represent this situation graphically.
Answer - 19 : -
Path of the train A = 3x + 4y – 12 = 0
Path of the train B = 6x + 8y – 48 = 0
Now, 3x + 4y – 12 = 0
Now plot the points (4, 0) and (0, 3) on the graph and join them to get a line, and 6x + 8y – 48 = 0
⇒ 6x = 48 – 8y
Now plot the points (0, 6) and (4, 3) on the graph and join themto get another line.
Answer - 20 : -
Present age of Aarushi = x years
and age of Ravish = y years
7 years ago,
age of Aarushi = x – 7
years and age of Ravish =y-7 years
∴ y- 7 = 7 (X – 7)
⇒ y – 7 = 7x – 49
⇒ 7x – y = -7 + 49 = 42
7x – y = 42
⇒ y = 7x – 42
If x = 6, then
y = 7 x 6 – 42 = 42 – 42 = 0,
If x = 7, then
y = 7 x 7 – 42 – 49 – 42 = -7
Plot the points (6, 0) (7, -7) on the graph and join them.
After 3 years,
age of Aarushi = x + 3
and age of Ravish = y + 3
⇒ y + 3 = 3(x + 3)
⇒ y + 3 = 3x + 9
⇒ y = 3x+ 9-3
⇒ y = 3x + 6
If x = -2, then y = 3 x (-2) + 6 =6-6=0
If x = 1, then y = 3 x (1) + 6 =3+6=9
Plot the points (1, 9), (-2, 0) on the graph Arundeep’s Mathematics (R.D.) 9th and join them to get another line.