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Find your Math Personality!
Draw the graphs of the equations x - y + 1 = 0 and 3x + 2y - 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
Solution:
By plotting the graph of two linear equations and x-axis, a triangle can be formed and shaded and hence, the vertices can be located.
x - y + 1 = 0
⇒ y = x + 1
x |
-1 |
2 |
y = x + 1 |
0 |
3 |
3x + 2y -12 = 0
⇒ 2y = 12 - 3x
⇒ y = (12 - 3x) / 2
x |
4 |
2 |
y = (12 - 3x) / 2 |
0 |
3 |
From the graph, the vertices of the triangle are (-1, 0), (4, 0), and (2, 3).
☛ Check: NCERT Solutions Class 10 Maths Chapter 3
Video Solution:
Draw the graphs of the equations x - y + 1 = 0 and 3x + 2y - 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis and shade the triangular region.
NCERT Solutions for Class 10 Maths - Chapter 3 Exercise 3.2 Question 7
Summary:
For the graphs of the equations x - y + 1 = 0 and 3x + 2y - 12 = 0, the coordinates of the vertices of the triangle formed by these lines and the x-axis are (-1, 0), (4, 0), and (2, 3).
☛ Related Questions:
- On comparing the ratios find out whether the following pair of linear a1/a2,b1/b2 and c1/c2, find out whether the following pair of linear equations are consistent, or inconsistent (i) 3x + 2 y = 5; 2x - 3y = 7 (ii) 2x - 3y = 8; 4x - 6 y = 9 (iii) 3/2x + 5/3y = 7; 9x -10y = 14 (iv) 5x - 3y = 11; -10x + 6 y = -22 (v) 4/3x + 2 y = 8; 2x + 3y = 12
- Which of the following pairs of linear equations are consistent / inconsistent? If consistent, obtain the Solution graphically: (i) x + y = 5, 2x + 2 y = 10 (ii) x - y = 8, 3x - 3y =16 (iii) 2x + y - 6 = 0, 4x - 2 y - 4 = 0 (iv) 2x - 2 y - 2 = 0, 4x - 4 y - 5 = 0
- Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
- Given the linear equation 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is: (i) intersecting lines (ii) parallel lines (iii) coincident lines
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