Question

What is the distance between the point (-5, -4) and the line 2x + 3y + 5 = 0

Answer 1

hello

points (-5,-4) to the line

• 5x-4y-1=0
• let x=-5 and y=-4
• Ax+By+C=0
• A=5
• B=-4
• c=1

Answer 2

Answer:

The distance between point an line is 3.62

Step-by-step explanation:

Given as :

The point is $x_1 y_1$  = - 5 , - 4

The line equation is 2 x + 3 y = - 5

The point which satisfy this line equation

for x = 0  , y = $\dfrac{-5}{3}$

for y = 0 , x = $\dfrac{-5}{2}$

So, The point which satisfy the line is $x_2 , y_2$  = $\dfrac{-5}{3}$  ,  $\dfrac{-5}{2}$

From distance formula

Distance = $\sqrt{(x_2-x_1)^{2} + (y_2-y_1)^{2} }$

Or, D = $\sqrt{(\frac{-5}{3} +5)^{2} + (\frac{-5}{2} +4)^{2} }$

Or, D = $\sqrt{(\frac{10}{3} )^{2} + (\frac{3}{2} )^{2} }$

Or, D = $\sqrt{\dfrac{100}{9}+\dfrac{9}{4} }$

∴    D = $\sqrt{\dfrac{481}{36} }$

i.e Distance = 3.65 unit

So, The distance between point and line = 3.62

Hence, The distance between point an line is 3.62  Answer