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Write the equation of the line through M and perpendicular to MN if M (3,-5) and N (5,6)

User Guilhebl
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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)

User Joey Hagedorn
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