Find graphically, the vertices of the triangle whose sides have the equations 2y - x = 8; 5y - x = 14 and y - 2x = 1 respectively.
Take 1 cm = 1 unit on both the axes.

Question

Find graphically, the vertices of the triangle whose sides have the equations 2y - x = 8; 5y - x = 14 and y - 2x = 1 respectively. Take 1 cm = 1 unit on both the axes.

KnowledgeBoat · Accepted Answer

First equation: 2y - x = 8 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -4, then 2y - (-4) = 8 ⇒ y = 2 Let x = -2, then 2y - (-2) = 8 ⇒ y = 3 Let x = 0, then 2y - 0 = 8 ⇒ y = 4 Let x = 2, then 2y - 2 = 8 ⇒ y = 5 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -4| -2| 0 | 2 --|---|---|---|-- y | 2 | 3 | 4 | 5 Step 3: Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph. Second equation: 5y - x = 14 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -4, then 5y - (-4) = 14 ⇒ y = 2 Let x = 0, then 5y - 0 = 14 ⇒ y = 2.8 Let x = 2, then 5y - 2 = 14 ⇒ y = 3.2 Let x = 4, then 5y - 4 = 14 ⇒ y = 3.6 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -4| 0 | 2 | 4 --|---|-- |---|-- y | 2 |2.8|3.2| 3.6 Step 3: Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph. Third equation: y - 2x = 1 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = 0, then y - 2 0 = 1 ⇒ y = 1 Let x = 2, then y - 2 2 = 1 ⇒ y = 5 Let x = 4, then y - 2 4 = 1 ⇒ y = 9 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | 0 | 2 | 4 --|---|---|--- y | 1 | 5 | 9 Step 3: Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph. The vertices of the triangle are: The coordinate of A = (2, 5) The coordinate of B = (-4, 2) The coordinate of C = (1, 3) Hence, the coordinates of the vertices of triangle = (1, 3), (-4, 2) and (2, 5).

Mathematics

Find graphically, the vertices of the triangle whose sides have the equations 2y - x = 8; 5y - x = 14 and y - 2x = 1 respectively.
Take 1 cm = 1 unit on both the axes.

Graphical Solution

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Mathematics

Find graphically, the vertices of the triangle whose sides have the equations 2y - x = 8; 5y - x = 14 and y - 2x = 1 respectively.Take 1 cm = 1 unit on both the axes.

Graphical Solution

Related Questions

Draw the graph of 3x + 2y = 6. Use the graph drawn to find the area of triangle formed by the line drawn and the co-ordinate axes.

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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).

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Find graphically, the vertices of the triangle whose sides have the equations 2y - x = 8; 5y - x = 14 and y - 2x = 1 respectively.
Take 1 cm = 1 unit on both the axes.

Use the graphical method to find the value of k, if :
(i) (k, -3) lies on the straight line 2x + 3y = 1
(ii) (5, k - 2) lies on the straight line x - 2y + 1 = 0

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).

Solve graphically, the following equations.
x + 2y = 4; 3x - 2y = 4.
Take 2 cm = 1 unit on each axis.
Also, find the area of the triangle formed by the lines and the x-axis.