Question

Find the distance from the point A(2,−1) to the line y = −x+4. Round your answer to the nearest tenth.

Answer 1

The distance from point A(2,-1) to the line y = -x + 4 is approximately 0.7 units.

Step-by-step explanation:

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

d = |Ax + By + C| / sqrt(A^2 + B^2)

In this case, the equation of the line is y = -x + 4, which can be rewritten as x + y - 4 = 0. So, A = 1, B = 1, and C = -4. Plugging these values into the formula and substituting the coordinates of point A(2,-1), we get:

d = |1*2 + 1*(-1) - 4| / sqrt(1^2 + 1^2) = |1| / sqrt(2) = 1 / sqrt(2) ≈ 0.7

Therefore, the distance from point A(2,-1) to the line y = -x + 4 is approximately 0.7 units.