Find, graphically, the coordinates of the vertices of the triangle formed by the lines:
8y - 3x + 7 = 0, 2x - y + 4 = 0 and 5x + 4y = 29.

Question

Find, graphically, the coordinates of the vertices of the triangle formed by the lines: 8y - 3x + 7 = 0, 2x - y + 4 = 0 and 5x + 4y = 29.

KnowledgeBoat · Accepted Answer

Given, ⇒ 8y - 3x + 7 = 0 ⇒ 8y = 3x - 7 ⇒ y = .........(1) When x = -3, y = = -2, x = 1, y = = -0.5 x = 5, y = = 1. Table of values of equation (1) : x | -3 | 1 | 5 ---- | ---- | ---- | ---- y | -2 | -0.5 | 1 Steps of construction : 1. Plot the points (-3, -2), (1, -0.5), (5, 1) on graph. 2. Join the points. Given, ⇒ 2x - y + 4 = 0 ⇒ y = 2x + 4 When x = -2, y = 2(-2) + 4 = -4 + 4 = 0, x = -1, y = 2(-1) + 4 = -2 + 4 = 2, x = 0, y = 2(0) + 4 = 0 + 4 = 4. Table of values of equation (2) : x | -2 | -1 | 0 ---- | ---- | ---- | ---- y | 0 | 2 | 4 Steps of construction : 1. Plot the points (-2, 0), (-1, 2), (0, 4) on graph. 2. Join the points. Given, ⇒ 5x + 4y = 29 ⇒ 4y = 29 - 5x ⇒ y = ..........(3) When x = 1, y = = 6, x = 3, y = = 3.5, x = 5, y = = 1. Table of values of equation (3) : x | 1 | 3 | 5 ---- | ---- | ---- | ---- y | 6 | 3.5 | 1 Steps of construction : 1. Plot the points (1, 6), (3, 3.5), (5, 1) on graph. 2. Join the points. From graph, These three lines intersect each other at (-3, -2), (5, 1) and (1, 6). Hence, the coordinates of the vertices of the triangle formed by these lines are (-3, -2), (5, 1) and (1, 6).

Mathematics

Find, graphically, the coordinates of the vertices of the triangle formed by the lines:
8y - 3x + 7 = 0, 2x - y + 4 = 0 and 5x + 4y = 29.

Coordinate Geometry

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Mathematics

Find, graphically, the coordinates of the vertices of the triangle formed by the lines:8y - 3x + 7 = 0, 2x - y + 4 = 0 and 5x + 4y = 29.

Coordinate Geometry

Related Questions

Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations: 6y = 5x + 10, y = 5x - 15. From the graph, find(i) the coordinates of the point where the two lines intersect.(ii) the area of the triangle between the lines and the x-axis.

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Find, graphically, the coordinates of the vertices of the triangle formed by the lines:
8y - 3x + 7 = 0, 2x - y + 4 = 0 and 5x + 4y = 29.

Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations: 6y = 5x + 10, y = 5x - 15. From the graph, find
(i) the coordinates of the point where the two lines intersect.
(ii) the area of the triangle between the lines and the x-axis.

Solve the following system of equations graphically :
x - 2y - 4 = 0, 2x + y - 3 = 0.