Question

find the length of perpendicular from the point (2,3) on the line 4x-6y-3=0​

Answer 1

We get the perpendicular distance = $\dfrac{\sqrt{13}}{2}$

Step-by-step explanation:

Since, we are given the equation of line as;

• 4x - 6y -3 = 0

• We are asked to find out the length of perpendicular from the point (2, 3) on the above line.

• We know that this distance would be the minimum distance between the given point and line.

• So, We assume the coordinates of point (2, 3) as x = 2 and y = 3.

Now, we write as:

Ax + By + C = 0 , compare this equation with the equation of line.

We get as;

A = 4, B = -6 and C = -3

Now, the length of perpendicular:

• d = $\dfrac{\left | Ax + By +C \right |}{\sqrt{A^2+B^2}}$

= $\dfrac{\left | (4 \times 2) + (-6 \times 3) + (-3) \right |}{\sqrt{4^2+(-6)^2}}$

= $\dfrac{\left | 8 - 18 + (-3) \right |}{\sqrt{16+36}}$

= $\dfrac{\left | -13 \right |}{\sqrt{52}}$

= $\dfrac{\sqrt{13}}{2}$

This is the perpendicular distance.

Thus, we get the perpendicular distance = $\dfrac{\sqrt{13}}{2}$

Answer 2

Answer:

Step-by-step explanation:

Since, we are given the equation of line as;

4x - 6y -3 = 0

We are asked to find out the length of perpendicular from the point (2, 3) on the above line.

We know that this distance would be the minimum distance between the given point and line.

So, We assume the coordinates of point (2, 3) as x = 2 and y = 3.

Now, we write as:

Ax + By + C = 0 , compare this equation with the equation of line.

We get as;

A = 4, B = -6 and C = -3