Answer:
Distance from point A(0,5) to y = -3 x - 5 is √10 units units.
Step-by-step explanation:
Here, the given line equation is y = -3x -5
Also, the point A (0,5) is the given point.
Now, a distance of a point (m,n) from a line Ax + By + c = 0 is given as:
[tex]d = \frac{\mid Am +bn+c \mid}{\sqrt{A^2 + B^2} }[/tex]
Here, the equation is y = -3 x -5
⇒ 3 x + y + 5 = 0 , here A = 3, B = 1
Now, the value of line equation at (0,5) is 3(0) + 5 + 5 = 10
So, from the given distance formula, we get:
[tex]d = \frac{\mid Am +bn+c \mid}{\sqrt{A^2 + B^2} } = d = \frac{10}{\sqrt{(3)^2 + (1)^2} } = \frac{10}{\sqrt{(10)}} = \sqrt{(10)}[/tex]
⇒ d = √10 units
Hence, distance from point A(0,5) to y = -3 x - 5 is √10 units units.
