Perpendicular Lines - Math

First, calculate the slope of the line segment between the given points.

We want a line that is perpendicular to this segment and passes through its midpoint. The slope of a perpendicular line is the negative inverse. The slope of the perpendicular bisector will be .

Next, we need to find the midpoint of the segment, using the midpoint formula.

Using the midpoint and the slope, we can solve for the value of the y-intercept.

Using this value, we can write the equation for the perpendicular bisector in slope-intercept form.

Find the slope of the line through the two points. It is .

Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is . Plug the slope and one of the points into the point-slope formula . Isolate for .

The slope of a perpendicular line is equal to the negative reciprocal of the original line. This means that the slope of our perpendicular line must be 3. We can also note that is also equal to 3, so both of these slopes are correct. The y-intercept does not matter, as the slope is the only thing that determines the slant of the line. Therefore, numerals I and III are both correct.

In order for two lines to be perpendicular to each other, their slopes must be opposites and reciprocals of each other, meaning the fraction must be flipped upside down and the signs must be changed. In this situation, the original equation had a slope of , so the perpendicular slope must be .

Two lines are perpendicular if they have opposite reciprocal slopes. When a line is in standard form, the is the slope. A perpendicular line will have a slope of .

The slope of our given line is . Therefore we want a slope of . The only line with the correct slope is .

First, find the slope of the original line, which is . You can do this by isolating for so that the equation is in slope-intercept form. Once you find the slope, just replace the in the original equation withe the negative reciprocal (perpendicular lines have a negative reciprocal slope for each other). Thus, your answer is

In order for two lines to be perpendicular, their slopes must be opposites and recipricals of each other. The first step is to find the slope of the given equation:

Therefore, the slope of the perpendicular line must be . Using the point-slope formula, we can find the equation of the new line:

Perdendicular lines have slopes that are opposite reciprocals. The slope of the old line is , so the new slope is .

Plug the new slope and the given point into the slope intercept equation to calculate the intercept:

or , so .

Thus , or .

The equation is given in the slope-intercept form, so we know the slope is . To have perpendicular lines, the new slope must be the opposite reciprocal of the old slope, or

Then plug the new slope and the point into the slope-intercept form of the equation:

so so

So the new equation becomes: and in standard form

The original line has a slope of , a line perpendicular to the original line will have a slope which is the negative reciprocal of this value.

Put this equation into slope-intercept form, y = mx + b, to find the slope, m.

Do this by subtracting from both sides of the equation:

The slope of this line is .

The slope of the perpendicular line is the negative reciprocal. Switch the numerator and denominator, and then multiply by :

Perpendicular lines have slopes that are the opposite reciprocals of each other. Thus, we first identify the slope of the given line, which is (since it is in the form , where represents slope).

Then, we know that any line which is perpendicular to this will have a slope of .

Thus, we can determine that is the only choice with the correct slope.

Isolate for so that the equation now reads

The slope is .

The definition of perpendicular lines is that their slopes are inverse reciprocals of one another. Since the slope in the given equation is , this means that the slope of its perpendicular line would be .

The answer

is the only equation listed that has a slope of .

The definition of perpendicular lines is that their slopes are inverse reciprocals of one another. Since the slope in the given equation is , this means that the slope of its perpendicular line would be .

The answer

is the only equation listed that has a slope of .

In standard form, the is the slope.

The slope of a perpendicular line is the negative reciprocal of the original line.

For our given line, the slope is . Therefore, the slope of the perpendicular line is .

In standard form, is the slope.

The slope of a perpendicular line is the negative reciprocal of the original line.

For our given line, the slope is . Therefore, the slope of the perpendicular line is .

Recall that the slopes of perpendicular lines are opposite reciprocals of one another. As a result, we are looking for the opposite reciprocal of . Thus, we can get that the opposite reciprocal is .

The slope of a perpendicular line is equal to the negative reciprocal of the original line. This means that the slope of our perpendicular line must be 3. We can also note that is also equal to 3, so both of these slopes are correct. The y-intercept does not matter, as the slope is the only thing that determines the slant of the line. Therefore, numerals I and III are both correct.