Question:

The lines x + 2y - 5 = 0, 2x - 3y + 4 = 0, 6x + 4y - 13 = 0

Updated On: Jul 7, 2022
  • are concurrent.
  • form a right angled triangle.
  • form an isosceles triangle
  • form an equilateral triangle
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The Correct Option is B

Solution and Explanation

Lines II and III are at right angles $[ \because \, (\frac{2}{3})(- \frac{3}{2}) = - 1$ Lines I and II intersect at the point (1, 2) and (1, 2) does not belong to III. Hence, the lines are not concurrent, i.e., they form a right angled triangle.
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Concepts Used:

Horizontal and vertical lines

Horizontal Lines:

  • A horizontal line is a sleeping line that means "side-to-side".
  • These are the lines drawn from left to right or right to left and are parallel to the x-axis.

Equation of the horizontal line:

In all cases, horizontal lines remain parallel to the x-axis. It never intersects the x-axis but only intersects the y-axis. The value of x can change, but y always tends to be constant for horizontal lines.

Vertical Lines:

  • A vertical line is a standing line that means "up-to-down".
  • These are the lines drawn up and down and are parallel to the y-axis.

Equation of vertical Lines:

The equation for the vertical line is represented as x=a,

Here, ‘a’ is the point where this line intersects the x-axis.

x is the respective coordinates of any point lying on the line, this represents that the equation is not dependent on y. 

Horizontal lines and vertical lines are perpendicular to each other.