Find graphically the coordinates of the vertices of the triangle formed by the lines y - 2 = 0, 2y + x = 0 and y + 1 = 3 (x - 2). Hence, find the area of the triangle formed by these lines.
Coordinate Geometry
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Find graphically the coordinates of the vertices of the triangle formed by the lines y - 2 = 0, 2y + x = 0 and y + 1 = 3 (x - 2). Hence, find the area of the triangle formed by these lines.

KnowledgeBoat · Accepted Answer

Given, ⇒ y - 2 = 0 ⇒ y = 2 ........(1) Given, ⇒ 2y + x = 0 ⇒ 2y = -x ⇒ y = - ............(2) When, x = -2, y = = 1, x = 0, y = = 0, x = 2, y = = -1. Table of equation (2) : x | -2 | 0 | 2 ---- | ---- | ---- | ---- y | 1 | 0 | -1 Steps of construction : 1. Plot the points (-2, 1), (0, 0), (2, -1) on graph. 2. Join the points. Given, ⇒ y + 1 = 3(x - 2) ⇒ y + 1 = 3x - 6 ⇒ y = 3x - 6 - 1 ⇒ y = 3x - 7 ...........(3) When x = 1, y = 3 × 1 - 7 = 3 - 7 = -4, x = 2, y = 3 × 2 - 7 = 6 - 7 = -1, x = 3, y = 3 × 3 - 7 = 9 - 7 = 2. Table of equation (3) : x | 1 | 2 | 3 ---- | ---- | ---- | ---- y | -4 | -1 | 2 Steps of construction : 1. Plot the points (1, -4), (2, -1), (3, 2) on graph. 2. Join the points. From graph, A(-4, 2), B(3, 2), C(2, -1) are the vertices of the triangle. From C, draw CD perpendicular to AB. As, 1 block = 1 unit. AB = 7 units and CD = 3 units Area of triangle = × base × height = × AB × CD = × 7 × 3 = = 10.5 sq. units Hence, coordinates of the vertices of the triangle are (-4, 2), (3, 2), (2, -1) and area = 10.5 sq. units.

Mathematics

Find graphically the coordinates of the vertices of the triangle formed by the lines y - 2 = 0, 2y + x = 0 and y + 1 = 3 (x - 2). Hence, find the area of the triangle formed by these lines.

Coordinate Geometry

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Mathematics

Find graphically the coordinates of the vertices of the triangle formed by the lines y - 2 = 0, 2y + x = 0 and y + 1 = 3 (x - 2). Hence, find the area of the triangle formed by these lines.

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.

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.

A line segment is of length 10 units and one of its end is (-2, 3). If the ordinate of the other end is 9, find the abscissa of the other end.

A(-4, -1), B(-1, 2) and C(α, 5) are the vertices of an isosceles triangle. Find the value of α given that AB is the unequal side.

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.

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.