A triangle is formed by the straight lines x + 2y - 3 = 0, 3x - 2y + 7 = 0 and y + 1 = 0. Find graphically :
(i) the co-ordinates of the vertices of the triangle.
(ii) the area of the triangle.

Question

A triangle is formed by the straight lines x + 2y - 3 = 0, 3x - 2y + 7 = 0 and y + 1 = 0. Find graphically : (i) the co-ordinates of the vertices of the triangle. (ii) the area of the triangle.

KnowledgeBoat · Accepted Answer

First equation: x + 2y - 3 = 0 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -1, then (-1) + 2y - 3 = 0 ⇒ y = 2 Let x = 0, then 0 + 2y - 3 = 0 ⇒ y = 1.5 Let x = 1, then 1 + 2y - 3 = 0 ⇒ y = 1 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -1 | 0 | 1 --|--- |---|--- y | 2 |1.5| 1 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 + 7 = 0 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -1, then 3 (-1) - 2y + 7 = 0 ⇒ y = 2 Let x = 0, then 3 0 - 2y + 7 = 0 ⇒ y = 3.5 Let x = 1, then 3 1 - 2y + 7 = 0 ⇒ y = 5 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -1 | 0 | 1 --|--- |---|--- y | 2 |3.5| 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. Third equation: y + 1 = 0 That is, y = - 1, x = 0 Draw a straight line parallel to x-axis with y = -1. (i) From the graph, the vertices of triangle ABC are A(-1, 2), B(5, -1) and C(-3, -1). (ii) Area of triangle = x base x height = x BC x AD = x 8 x 3 = 4 x 3 = 12 sq. units. Hence, area of the triangle = 12 sq. units.

Mathematics

A triangle is formed by the straight lines x + 2y - 3 = 0, 3x - 2y + 7 = 0 and y + 1 = 0. Find graphically :
(i) the co-ordinates of the vertices of the triangle.
(ii) the area of the triangle.

Graphical Solution

Related Questions

On the same graph paper, draw the straight lines represented by equations:
x = 5, x + 5 = 0, y + 3 = 0 and y = 3.
Also, find the area and perimeter of the rectangle formed by the intersection of these lines.

On a graph paper, mark the points A(-1, -1) and B(2, 5). Draw a straight line passing through A and B. If points (m, 4) and (0.5, n) lie on this line, use graphical method of finding the values of m and n.

Find the distance between the points (2, -5) and (7, 7).

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Mathematics

A triangle is formed by the straight lines x + 2y - 3 = 0, 3x - 2y + 7 = 0 and y + 1 = 0. Find graphically :(i) the co-ordinates of the vertices of the triangle.(ii) the area of the triangle.

Graphical Solution

Related Questions

On the same graph paper, draw the straight lines represented by equations:x = 5, x + 5 = 0, y + 3 = 0 and y = 3.Also, find the area and perimeter of the rectangle formed by the intersection of these lines.

On a graph paper, mark the points A(-1, -1) and B(2, 5). Draw a straight line passing through A and B. If points (m, 4) and (0.5, n) lie on this line, use graphical method of finding the values of m and n.

Find the distance between the points (2, -5) and (7, 7).

If A = (x, -7), B = (2, 5) and AB = 13 units, find x.

A triangle is formed by the straight lines x + 2y - 3 = 0, 3x - 2y + 7 = 0 and y + 1 = 0. Find graphically :
(i) the co-ordinates of the vertices of the triangle.
(ii) the area of the triangle.

On the same graph paper, draw the straight lines represented by equations:
x = 5, x + 5 = 0, y + 3 = 0 and y = 3.
Also, find the area and perimeter of the rectangle formed by the intersection of these lines.