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Determine, algebraically, the vertices of the triangle formed by the lines, 3x - y = 3; 2x - 3y = 2; x + 2y = 8

Solution:

From the above question, we have the equation as,

3x-y = 3 --------------(1)

2x - 3y = 2------------(2)

x + 2y = 8-------------(3)

Let us consider that lines (1), (2), and (3) represent the sides of a ∆ABC, i.e. AB, BC, and CA, respectively.

Solving lines (1) and (2), intersecting point B can be found

Multiplying (1) by 3 and Subtracting (2),

(9x - 3y) - (2x - 3y) = 9 - 2

7x = 7

x = 1.

Substitute the value of x in (1), we get,

3 x 1 - y = 3

y = 0.

Coordinates of point or vertex B are (1, 0).

Solving lines (2) and (3), intersecting point C can be found

Multiplying (3) by 2 and then Subtracting, (2), we get,

(2x + 4y) - (2x - 3y) = 16 - 2

7y = 14

y = 2.

Substitute the value of y in(3), we get,

x + 2 x 2 = 8 ⇒ x = 8 - 4

x = 4.

The coordinates of point or vertex C are (4,2).

Solving lines (3) and (1), we will get the intersecting point A.

Multiplying in (1) by 2 and then adding (3), we get,

(6x - 2y) + (x + 2y) = 6 + 8

7x = 14

x = 2.

Substituting the value of x in (1), we get,

3 x 2 - y = 3

y = 6 - 3

y = 3.

The coordinate of point or vertex A is (2, 3).

Therefore,the vertices of the ∆ABC formed by the given lines are A(2, 3), B( 1, 0) and C(4, 2).

✦ Try This: Determine, algebraically, the vertices of the triangle formed by the lines, 2x - y = 2; 2x - 3y = 1; x + 2y = 4

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.4 Problem 5

Summary:

Algebraically, the vertices of the triangle formed by the lines, 3x - y = 3; 2x - 3y = 2; x + 2y = 8 are A(2, 3), B( 1, 0) and C(4, 2).

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