Advertisements
Advertisements
प्रश्न
The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.
Find, graphically :
(i) the area of a triangle;
(ii) the coordinates of the vertices of the triangle.
Advertisements
उत्तर
y - 2 = 0
⇒ y = 2
y + 1 = 3(x - 2)
⇒ y + 1 = 3x - 6
⇒ y = 3x - 6 - 1
⇒ y = 3x - 7
The table for y + 1 = 3(x - 2) is
| X | 1 | 2 | 3 |
| Y | - 4 | - 1 | 2 |
Also we have
x + 2y = 0
⇒ x = - 2y
The table for x + y = 0 is
| X | - 4 | 4 | - 6 |
| Y | 2 | - 2 | 3 |
Plotting the above points we get the folllowing required graph:
(i) The area of the triangle ABC = `(1)/(2) xx "AB" xx "CD"`
= `(1)/(2) xx 7 xx 3`
= `(21)/(2)`
= 10.5 sq.units
(ii) The coordinates of the verticles of the triangle are ( - 4, 2), (3, 2) and (2, -1).
APPEARS IN
संबंधित प्रश्न
Solve graphically the simultaneous equations given below. Take the scale as 2 cm = 1 unit on both the axes.
x - 2y - 4 = 0
2x + y = 3
The cost of manufacturing x articles is Rs. (50 + 3x). The selling price of x articles is Rs. 4x.
On a graph sheet, with the same axes, and taking suitable scales draw two graphs, first for the cost of manufacturing against no. of articles and the second for the selling price against the number of articles.
Use your graph to determine:
No. of articles to be manufactured and sold to break even (no profit and no loss).
Using the same axes of co-ordinates and the same unit, solve graphically :
x + y = 0 and 3x - 2y = 10.
(Take at least 3 points for each line drawn).
Use the graphical method to find the value of 'x' for which the expressions `(3x + 2)/(2) and (3)/(4)x - 2`
Solve the following equations graphically :
x + 4y + 9 = 0
3y = 5x - 1
Solve the following system of equations graphically
x - y + 1 = 0
4x + 3y = 24
Solve the following system of equations graphically:
2x = 23 - 3y
5x = 20 + 8y
Also, find the area of the triangle formed by these lines and x-axis in each graph.
Solve graphically
y = 2x + 1, y + 3x – 6 = 0
Solve graphically
x = −3, y = 3
Two cars are 100 miles apart. If they drive towards each other they will meet in 1 hour. If they drive in the same direction they will meet in 2 hours. Find their speed by using graphical method.
