MHB Find an equation of the line that is perpendicular to x - y + 2 = 0

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To find the equation of a line perpendicular to x - y + 2 = 0 and passing through (3,1), the slope of the original equation is determined to be 1, making the perpendicular slope -1. The point-slope formula is then used with the point (3,1) and the slope -1, resulting in the equation y = -x + 4. This can be rearranged into standard form, yielding x + y - 4 = 0. The discussion emphasizes the importance of using the correct forms and methods for deriving the equations.
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Find an equation of the line that is perpendicular to x - y + 2 = 0 and passes through the point (3,1). Write your answer in two forms: y = mx + b and Ax + By + C = 0.

The equation we want is perpendicular to the given equation. This means the slope must be the negative reciprocal of the slope of the given equation.

True?

Steps:

1. Solve the given equation for y.

2. Find the negative reciprocal slope of the equation in step 1.

3. Plug the slope from step 2 and the point (3,1) into the point-slope formula and solve for y.

4. Express the equation in the form Ax + By + C = 0

Correct?
 
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For step 3, don't you mean "solve for b" instead of "solve for y"? (Wondering)

Other than that detail, I am in agreement with what you have posted. :)
 
greg1313 said:
For step 3, don't you mean "solve for b" instead of "solve for y"? (Wondering)

Other than that detail, I am in agreement with what you have posted. :)

Why solve for b in step 3? The slope m is required for the needed equation not the y-intercept or b.
 
Sorry; I mistook "point-slope" for "slope-intercept". At any rate, I don't see why you'd use point-slope when slope-intercept and standard form are required. Also, slope-intercept seems easier to work with.
 
Cool.
 
Steps:

1. Solve the given equation for y.

x - y + 2 = 0

x - y = - 2

- y = - x - 2

y = (- x - 2)/(-1)

y = x + 2

2. Find the negative reciprocal slope of the equation in step 1.

The negative reciprocal of 1 is - 1. This is our slope.

3. Plug the slope from step 2 and the point (3,1) into the point-slope formula and solve for y.

y - 1 = -(x - 3)

y - 1 = - x + 3

y = - x + 3 + 1

y = - x + 4

4. Express the equation in the form Ax + By + C = 0.

x + y - 4 = 0
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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