Answer:
The distance from point A(-9, -3) to the line y = x - 6 is 6√2 units.
Explanation:
To find the distance from point A(-9, -3) to the line y = x - 6, you can use the formula for the distance between a point (x₁, y₁) and a line Ax + By + C = 0:
Distance = |Ax₁ + By₁ + C| / √(A² + B²)
In this case, the equation of the line y = x - 6 can be written in the form Ax + By + C = 0. Here, A = -1 (the coefficient of x), B = 1 (the coefficient of y), and C = 6. The point A(-9, -3) can be considered as (x₁, y₁), with x₁ = -9 and y₁ = -3.
Now, plug these values into the formula:
Distance = |(-1)(-9) + (1)(-3) + 6| / √((-1)² + (1)²)
Distance = |9 - 3 + 6| / √(1 + 1)
Distance = |12| / √2
Distance = 12 / √2
To rationalize the denominator, multiply both the numerator and denominator by √2:
Distance = (12 / √2) * (√2 / √2)
Distance = (12√2) / 2
Distance = 6√2
So, the distance from point A(-9, -3) to the line y = x - 6 is 6√2 units.