Question

Find the distance of the point (0, -1) from the line joining the points (1,3) and (-2, 6)​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The correct answer is : 3 / sqrt(2)

Step-by-step explanation:

To find the distance of the point (0, -1) from the line joining the points (1,3) and (-2, 6), we can use the formula for the distance from a point to a line.

First, we need to find the equation of the line  passing through the points (1,3) and (-2,6). The slope of the line is:

m = (6-3)/(-2-1) = -1

Using point-slope form:

y - 3 = -1(x - 1)

Simplifying this equation, we get:

y = -x + 4

Now, we can find the perpendicular distance from the point (0, -1) to this line. We know that:

$d = |Ax1 + By1 + C| / (A^2 + B^2)^{2}$

In this case, $A = -1, B = 1, C = 4.$. Substituting the values of (x1, y1) as (0, -1), we get:

d = |(-1)(0) + (1)(-1) + 4| / sqrt((-1)^2 + 1^2)

Simplifying this, we get:

d = 3 / sqrt(2)

Therefore, the distance of the point (0, -1) from the line joining the points (1,3) and (-2, 6) is 3/sqrt(2) units.

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