Question

Find the distance from the point (-1,6) to the line y = -2x. Round to the nearest tenth, if necessary.

The distance is about
units.

Answer 1

To find the distance from a point to a line, you can use the formula:

Distance = |Ax + By + C| / √(A^2 + B^2)

In this case, the equation of the line is y = -2x, which can be rewritten as 2x + y = 0. So, A = 2, B = 1, and C = 0.

Now, plug the values into the formula:

Distance = |2(-1) + 1(6) + 0| / √(2^2 + 1^2)

Distance = |-2 + 6| / √(4 + 1)

Distance = 4 / √5

Now, round to the nearest tenth:

Distance ≈ 4 / 2.236 ≈ 1.8 units (rounded to the nearest tenth).

The distance is approximately 1.8 units.