Use graph paper for this question. Take 2 cm = 1 unit on both the axes.
(i) Draw the graphs of x + y + 3 = 0 and 3x - 2y + 4 = 0. Plot only three points per line.
(ii) Write down the co-ordinates of the point of intersection of the lines.
(iii) Measure and record the distance of the point of intersection of the lines from the origin in cm.

Question

Use graph paper for this question. Take 2 cm = 1 unit on both the axes.
(i) Draw the graphs of x + y + 3 = 0 and 3x - 2y + 4 = 0. Plot only three points per line.
(ii) Write down the co-ordinates of the point of intersection of the lines.
(iii) Measure and record the distance of the point of intersection of the lines from the origin in cm.

KnowledgeBoat · Accepted Answer

(i) First equation: x + y + 3 = 0 Step 1: Give three suitable values to the variable x and find the corresponding values of y. Let x = 0, then 0 + y + 3 = 0 ⇒ y = -3 Let x = -4, then -4 + y + 3 = 0 ⇒ y = 1 Let x = -6, then -6 + y + 3 = 0 ⇒ y = 3 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | 0 | -4| -6 --|---|---|--- y | -3| 1 | 3 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: 3x - 2y + 4 = 0 Step 1: Give three suitable values to the variable x and find the corresponding values of y. Let x = 0, then 3 0 - 2y + 4 = 0 ⇒ y = 2 Let x = 2, then 3 2 - 2y + 4 = 0 ⇒ y = 5 Let x = 4, then 3 4 - 2y + 4 = 0 ⇒ y = 8 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | 0 | 2 | 4 --|---|---|--- y | 2 | 5 | 8 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. (ii) Both the straight line drawn meet at the point A. As it is clear from the graph, co-ordinates of the common point A are (-2, -1). Hence, co-ordinates of the point of intersection of the lines are (-2, -1). (iii) In triangle OAB, Using pythagoras theorem, OA2 = AB2 + OB2 = 22 + 12 = 4 + 1 = 5 OA = OA = 2.2 cm Hence, the distance of the point of intersection of the lines from the origin is 2.2 cm.

Mathematics

Graphical Solution

Related Questions

Use graph paper for this question. Draw the graph of 2x - y - 1 = 0 and 2x + y = 9 on the same axes. Use 2 cm = 1 unit on both axes and plot only 3 points per line.
Write down the co-ordinates of the point of intersection of the two lines.

Use graph paper for this question. Take 2 cm = 2 units on x-axis and 2 cm = 1 unit on y-axis.
Solve graphically the following equations :
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The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.
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By drawing a graph for each of the equations 3x + y + 5 = 0; 3y - x = 5 and 2x + 5y = 1 on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point).
Take 2 cm = 1 unit on both the axes.

Mathematics

Graphical Solution

Related Questions

Use graph paper for this question. Draw the graph of 2x - y - 1 = 0 and 2x + y = 9 on the same axes. Use 2 cm = 1 unit on both axes and plot only 3 points per line.Write down the co-ordinates of the point of intersection of the two lines.

Use graph paper for this question. Take 2 cm = 2 units on x-axis and 2 cm = 1 unit on y-axis.Solve graphically the following equations :3x + 5y = 12; 3x - 5y + 18 = 0(Plot only three points per line)

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 triangle;(ii) the co-ordinates of the vertices of the triangle.

By drawing a graph for each of the equations 3x + y + 5 = 0; 3y - x = 5 and 2x + 5y = 1 on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point).Take 2 cm = 1 unit on both the axes.

Use graph paper for this question. Draw the graph of 2x - y - 1 = 0 and 2x + y = 9 on the same axes. Use 2 cm = 1 unit on both axes and plot only 3 points per line.
Write down the co-ordinates of the point of intersection of the two lines.

Use graph paper for this question. Take 2 cm = 2 units on x-axis and 2 cm = 1 unit on y-axis.
Solve graphically the following equations :
3x + 5y = 12; 3x - 5y + 18 = 0
(Plot only three points per line)

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 triangle;
(ii) the co-ordinates of the vertices of the triangle.

By drawing a graph for each of the equations 3x + y + 5 = 0; 3y - x = 5 and 2x + 5y = 1 on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point).
Take 2 cm = 1 unit on both the axes.