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Find the vertices of the triangle formed by the lines $4 x − y − 8 = 0$ , $2 x − 3 y + 6 = 0$ with the X-axis.

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(6, 2), (− 5, 0) and (3,2)

(7, 5), (− 4, 0) and (1,1)

(3, 4), (− 3, 0) and (2,0)

(1, 2), (− 1, 0) and (3,0)

answer is C.

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Detailed Solution

The point of intersection of both the lines and with x-axis gives vertices of the triangle.
Given pairs of equations are

4 x − y − 8 = 0 … (i) 2 x − 3 y + 6 = 0 … (i i)

Now to determine the vertices of triangle formed by a pair of equations and x-axis
The graphical representation is:
Question Image

The point of intersection of both the lines and with x-axis gives vertices of the triangle.
As both lines intersect at

3, 4

and with the x-axis at

(− 3, 0)

and

(2, 0)

Therefore, the vertices of the triangle formed by a pair of equations and x-axis are

(3, 4), (− 3, 0) and (2,0)

.
Hence, option (3) is correct.

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