Question

In the given figure, the equation of AB is 2y-3x=6. Find the co ordinates of A and B.​

Answer 1

In the given figure, Let the point of which the coordinate is given as (4,0) be C

So,

⇒ ∠ACB = 90°

Since, The line segment BC is perpendicular to the x-axis, Therefore the Abscissa of point B would be 4 (Same as of C)

Now, We just need to find the ordinate of the point B to get the coordinate of the point.

But, The equation of line is given,

⇒ 2y - 3x = 6 [ given ]

Put, x = 4

⇒ 2y - 3×4 = 6

⇒ 2y = 18

⇒ y = 9

Hence, Coordinate of point B is (4,9)

Similarly, At point A it is clear that it is on the x-axis therefore the ordinate of this specific point is 0.

Using the equation of the line given in the question,

⇒ 2×0 - 3x = 6

⇒ -3x = 6

⇒ x = -2

Hence, Coordinate of point A is (-2,0)