Find the distance from the point (-3,6) to the line y=-3/2x-5

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Answer 1

Answer: To find the distance from the point (-3,6) to the line y = -3/2x -5, we can use the formula for the distance between a point and a line. The formula is:

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

In this case, A = -3/2, B = 1, and C = 5. Substituting these values into the formula and plugging in the coordinates of the point (-3,6), we get:

distance = |-3/2(-3) + 1(6) + 5| / sqrt((-3/2)^2 + 1^2)

Simplifying further, we get:

distance = |9/2 + 6 + 5| / sqrt(9/4 + 1)

Simplifying the fraction under the square root, we get:

distance = |9/2 + 6 + 5| / sqrt(9/4 + 4/4)

Continuing to simplify, we get:

distance = |9/2 + 6 + 5| / sqrt(13/4)

Calculating further, we get:

distance = |9/2 + 6 + 5| / sqrt(13)/2

Finally, simplifying and calculating, we get:

distance = |9/2 + 6 + 5| / sqrt(13)/2 = 20/ sqrt(13) ≈ 5.44 units

So, the distance from the point (-3,6) to the line y = -3/2x -5 is approximately 5.44 units.

Find the distance from the point (-3,6) to the line y=-3/2x-5

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