Question

Find the distance from point A to the given line. Round your answer to the nearest tenth. y=-4x A(6,-2)

the distance is about ___ units.

Answer 1

To find the distance from point A (6, -2) to the line y = -4x, rearrange the line's equation into standard form and apply the distance formula. The calculation yields approximately 5.3 units as the distance.

Step-by-step explanation:

To find the distance from point A to the line y = -4x, we need to use the formula for the perpendicular distance from a point to a line. The formula for the distance d from a point (x1, y1) to a line Ax + By + C = 0 is:

d = |Ax1 + By1 + C| / √(A2 + B2)

First, we need to rearrange the equation of the given line into the standard form:

y + 4x = 0 (where A = 4, B = 1, and C = 0)

Now we can plug in the point A(6, -2) and coefficients into the distance formula:

d = |4*6 + 1*(-2) + 0| / √(42 + 12)

d = |24 - 2| / √(16 + 1)

d = 22 / √17

d ≈ 5.3

Therefore, the distance from point A to the line y = -4x is approximately 5.3 units.