Answer:
y + 5 = (-2/11)(x - 3)
Explanation:
To determine the equation of the line passing through point M(3, -5) and perpendicular to line segment MN, we need to find the negative reciprocal of the slope of MN.
First, we calculate the slope of line MN using the formula:
slope = (change in y) / (change in x)
By substituting the coordinates of M(3, -5) and N(5, 6) into the formula, we can determine the slope of MN:
slope of MN = (6 - (-5)) / (5 - 3) = 11 / 2
To obtain the negative reciprocal, we simply invert the fraction and change the sign:
negative reciprocal = -2/11
Now we have the slope of the line perpendicular to MN. We can proceed to use the point-slope form of a linear equation to express the equation of the line passing through M(3, -5):
y - y1 = m(x - x1)
Replacing the values with M(3, -5) and the negative reciprocal slope, we have:
y - (-5) = (-2/11)(x - 3)
Simplifying the equation gives the final form:
y + 5 = (-2/11)(x - 3)